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31b12a32e57f592b5120b874140e3e4d32dea046 | the conowingo dam, and to a lesser extent | the conowingo dam, and to a lesser extent the holtwood and safe harbor dams further upstream, stopped migratory fish species, especially american shad, from swimming further up the susquehanna river to spawn. in 1984, a fish capture feature was added at conowingo and shad were trucked upstream above all three dams and ... | wikipedia |
92faa90a8752ddd35edb38933837731a08a23601 | the river water impounded by the dam forms | the river water impounded by the dam forms the 14-mile (23 km) long conowingo reservoir, known locally as conowingo lake. the reservoir is used as a drinking water supply for baltimore and the chester water authority; as cooling water for the peach bottom nuclear generating station; and for recreational boating and fis... | wikipedia |
0db8b14f1e9c23548ad31a1a7c666397d00b9672 | on july 26, 2018, 20 of the 53 | on july 26, 2018, 20 of the 53 floodgates were opened due to rising floodwaters resulting from several days of torrential downpours in the mid-atlantic. the susquehanna river saw water levels of over 26.25 feet (8.00 m), placing nearby cities, like port deposit, at risk of flooding like in 2011. the ecological impact o... | wikipedia |
58e2313da5bb031a200da7f9c19f288bd2fe8bfb | on september 9, 2011, 44 flood gates were | on september 9, 2011, 44 flood gates were opened due to the impact of the remnants of tropical storm lee. the susquehanna river level behind the dam was 32.41 feet (9.88 m), the third-highest in history. the town of port deposit, located 5 miles southeast of the dam, was evacuated. | wikipedia |
5e520c725f347946ecc3d30d96fd60c360290d68 | in 1936, all the floodgates were opened for | in 1936, all the floodgates were opened for the first time. during hurricane agnes, in june 1972, all 53 floodgates were opened, for only the second time, and explosives planted to blow a section of the weir, as the waters rose during the early morning hours of june 24 within 5 feet (1.52 m) of topping the dam (a recor... | wikipedia |
012314e5655480e6ed3fedbffc818cca21fb3071 | the dam has 53 flood control gates, starting | the dam has 53 flood control gates, starting at the northeastern end of the powerhouse and spanning the majority of the dam. the floodgates are operated by three overhead cranes rated for 60 short tons (53.6 long tons; 54.4 t) each which were originally built by the morgan engineering company of ohio. the cranes run on... | wikipedia |
35d00145ebb47cd7e5ff1f6789603615ae3d3a04 | through subsidiaries and mergers, the dam is now | through subsidiaries and mergers, the dam is now operated by the susquehanna electric company, which is part of constellation energy. the current federal energy regulatory commission license for the dam was issued in 2021 and expires in 2071. | wikipedia |
846e256c3de184bc7a28aedbd4d81d42b600dd99 | the dam was built with 11 turbine sites, | the dam was built with 11 turbine sites, although only 7 turbines were initially installed, driving generators each rated for 36 megawatts. a turbine house, on the southwestern end of the dam, encloses these seven units. one additional "house" unit provides 25 hz power for the dam's electric railroad system (identical ... | wikipedia |
e9788b8ce6b9edd7975f594df4930ae3cab54c24 | when maryland public television aired its documentary, "conowingo | when maryland public television aired its documentary, "conowingo dam: power on the susquehanna" for chesapeake bay week in april 2016, the question came up about how many workers died performing their duties. while investigating the death of hunter h. bettis on november 26, 1927, darlington coroner wiliam b. selse com... | wikipedia |
aeddd48febe6ba1ec37fae0d09caff0cbe5ca6c6 | some 5,000 workers flocked to this rural northeastern | some 5,000 workers flocked to this rural northeastern corner of maryland, seeking to earn good pay as construction got underway. in addition to those working directly on the dam, large numbers relocated railroad tracks, paved new roads, and constructed steel towers to stretch the heavy transmission lines toward philade... | wikipedia |
f6c2aca37a95b1573831ccfaac5cdb672c2c4f06 | on january 23, 1925, philadelphia electric company awarded | on january 23, 1925, philadelphia electric company awarded the construction contract for the dam to stone & webster of boston, who did the design. construction, which started in 1926, was carried out by the arundel corporation of maryland. (abandoned railroad tracks for transporting heavy equipment to the dam site can ... | wikipedia |
7c173f7a82980d6713ad3fe972e274cf0592c8be | the dam supports a 9,000-acre reservoir, which today | the dam supports a 9,000-acre reservoir, which today covers the original town of conowingo. during dam construction, the town was moved to its present location about 1 mile (1.6 km) northeast of the dam's eastern end. the rising water also would have covered conowingo bridge, the original u.s. route 1 crossing, so it w... | wikipedia |
bdb378a0c38b434c6e5e6eed361a31a95e17ecca | the dam sits about 9.9 miles (16 km) | the dam sits about 9.9 miles (16 km) from the river mouth at the chesapeake bay, 5 miles (8 km) south of the pennsylvania border and 45 miles (72 km) northeast of baltimore, on the border between cecil and harford counties. | wikipedia |
bf0b3ef932890b33d29144c5a8061258c03db4f2 | the conowingo dam (also conowingo hydroelectric plant, conowingo | the conowingo dam (also conowingo hydroelectric plant, conowingo hydroelectric station) is a large hydroelectric dam in the lower susquehanna river near the town of conowingo, maryland. the medium-height, masonry gravity dam is one of the largest non-federal hydroelectric dams in the u.s., and the largest dam in the st... | wikipedia |
c20774de8f9a79783af22cb6b4629f82da0162e7 | greenewalt and his wife margaretta (née du pont) | greenewalt and his wife margaretta (née du pont) had two sons, crawford "greenie" greenewalt jr. (1937-2012) and david greenewalt, and daughter, nancy l. frederick. the younger crawford was a professor of classical archaeology at the university of california, berkeley who was among the leaders of the archaeological exp... | wikipedia |
d4b6125e9321548536443e3f2d461f694abf00be | his widely varied interests included ornithology and high-speed | his widely varied interests included ornithology and high-speed photography via his friend harold e. "doc" edgerton. greenewalt published a book of 70 high-speed photographs of hummingbirds in 1960 (greenewalt, c.h. 1960. hummingbirds doubleday & co., garden city, new york.). and later, dimensional relationships for fl... | wikipedia |
842200fa59ac466edc9151c4507a819a05d9a111 | crawford hallock greenewalt was born in cummington, massachusetts, | crawford hallock greenewalt was born in cummington, massachusetts, the son of frank lindsay greenewalt and mary hallock-greenewalt, an inventor and pianist born in beirut. in 1922, he earned a bachelor of science degree in chemical engineering from massachusetts institute of technology, where he joined theta chi frater... | wikipedia |
499950442462925984a7951cb1646357c04157b8 | crawford hallock greenewalt (august 16, 1902 – september | crawford hallock greenewalt (august 16, 1902 – september 28, 1993) was an american chemical engineer who was president of the dupont company from 1948 to 1962, and chairman from 1962 to 1967. | wikipedia |
4f22b9b2767edba757ffd73609dcf41ec608649a | schmidt (1936) gave an example of an analytically | schmidt (1936) gave an example of an analytically ramified reduced local ring. krull showed that every 1-dimensional normal noetherian local ring is analytically unramified; more precisely he showed that a 1-dimensional normal noetherian local domain is analytically unramified if and only if its integral closure is a f... | wikipedia |
8299b784e7b5414a0375c375777a9e8c3a48d259 | let k be a perfect field of characteristic | let k be a perfect field of characteristic 2, such as f.let k be k ({ u, v : n ≥ 0}), where the u and v are indeterminates.let t be the subring of the formal power series ring k ] generated by k and k ] and the element Σ(u x + v y). nagata proves that t is a normal local noetherian domain whose completion has nonzero n... | wikipedia |
3c1cb5c3f2a700c9519dd1f5abc3eec65fcd2923 | there are two classical theorems of david rees | there are two classical theorems of david rees (1961) that characterize analytically unramified rings. the first says that a noetherian local ring (r, m) is analytically unramified if and only if there are a m -primary ideal j and a sequence n j → ∞ {\displaystyle n_{j}\to \infty } such that j j ¯ ⊂ j n j {\displaystyl... | wikipedia |
aa7ec8cc71ac2ee4401d9afe178ed404166d12a9 | chevalley (1945) showed that every local ring of | chevalley (1945) showed that every local ring of an algebraic variety is analytically unramified. schmidt (1936) gave an example of an analytically ramified reduced local ring. krull showed that every 1-dimensional normal noetherian local ring is analytically unramified; more precisely he showed that a 1-dimensional no... | wikipedia |
2e161bca9d820620f21acd47f3ea619b6b9fa9ac | alexander aronovich feldbaum was a soviet scientist in | alexander aronovich feldbaum was a soviet scientist in the field of automatic control and fundamental computer science. he is one of the founders of optimal control, and proposed dual control theory in the study of self-adjusting and self-learning systems. | wikipedia |
ae48001f6358c164f248fe0d18c6537cdcf6eaca | from 1961, he was the head of the | from 1961, he was the head of the laboratory of self-tuning systems at the institute of automation and telemechanics of the ussr academy of sciences. at the institute of automation and telemechanics of the ussr academy of sciences, he established a laboratory for search and self-tuning systems, where the world's first ... | wikipedia |
afedc860a88871295756a8722827361b0d0f8e73 | a. a. feldbaum considered the general problem of | a. a. feldbaum considered the general problem of synthesizing optimal systems, introducing the fundamental concept of a switching surface in phase space (1955). sometime later, sun zhen, a graduate student of a. a. feldbaum from china, simulated this switching surface on a computer. subsequently, this model was used in... | wikipedia |
72dffcd39d1434be3a57befbc8600390384a61b4 | in 1955, at several seminars at the ras | in 1955, at several seminars at the ras v. a. steklov mathematical institute, a. a. feldbaum extensively discussed his findings. he explained and posed the general problem of optimal control to a group of outstanding mathematicians led by academician l. s. pontryagin. | wikipedia |
d8fd39e8f5a03785ca3e32a08a61ffb3b1541cad | in 1953, a. a. feldbaum defended his doctoral | in 1953, a. a. feldbaum defended his doctoral dissertation on the dynamics of automatic regulation systems. a. a. feldbaum introduced the concept of the degree of oscillation of transitional processes, proved a number of theorems about the forms of transient processes and their relationship with the distribution of the... | wikipedia |
75053d4235b7561650026ad558222d16f9b0e601 | since 1945, a. a. feldbaum taught at the | since 1945, a. a. feldbaum taught at the peter the great military academy of the strategic missile forces, a professor of the department of missile control systems of the faculty of reactive armament. he was engaged in the development of the theory of linear control systems, as well as the development and creation of t... | wikipedia |
917ef80d5a95c7b601f1504db41c9abd49600a4d | since 1936, a. a. feldbaum has been an | since 1936, a. a. feldbaum has been an employee of the all-russian electrotechnical institute (Всероссийский электротехнический институт). in 1939, he published his first scientific paper dedicated to the theory of automatic control. in 1943, he defended his phd thesis on the theory of controlling devices. | wikipedia |
20eacfb559caee8a3b5d2f41b28eea41fa9a762d | in 1924, he entered directly into the fifth | in 1924, he entered directly into the fifth grade of middle school. in 1937, he graduated from the moscow power engineering institute, and in 1941, the correspondence department of the msu faculty of mechanics and mathematics. | wikipedia |
54aa1bf30ca19e97417d5af1ba45d1f0ecdc9d5a | alexander aronovich feldbaum (1913 — 1969) was a | alexander aronovich feldbaum (1913 — 1969) was a soviet scientist in the field of automatic control and fundamental computer science. he is one of the founders of optimal control, and proposed dual control theory in the study of self-adjusting and self-learning systems. | wikipedia |
e970c5717b199992df397307b4b7741a3c234a91 | the arado ar 79 was an aerobatic two-seat | the arado ar 79 was an aerobatic two-seat trainer and touring aircraft designed and produced by the german aircraft manufacturer arado. it was the final civilian aircraft developed by the company. the ar 79 was developed during the mid-1930s as a successor to the arado l i and arado l ii touring aircraft by the aeronau... | wikipedia |
b3d62846d7441fdb32c8f0cbe7de2d88c156044d | furthermore, the ar 79 placed well in numerous | furthermore, the ar 79 placed well in numerous air races; on 31 july 1938, one aircraft took first place in race a of the international air races held at frankfurt. individual aircraft were acquired by various german figures, including ernst udet, hanna reitsch, heinz rühmann, alfried krupp von bohlen und halbach, and ... | wikipedia |
e32db0625fe7df8ef67b3475185d7ed55faafe06 | a pair of prototypes, d-ekcx and d-ehcr, were | a pair of prototypes, d-ekcx and d-ehcr, were commenced test flying in april 1938. they quickly drew attention via the setting of multiple world speed records in their class that same year, specifically, on 15 july, the solo 1,000 km (621.4 mi) at 229.04 km/h (142.32 mph); on 29 july, the 2,000 km (1,242.8 mi) at 227.0... | wikipedia |
9ce0ece73a3023f92361d89c8ea1e0f4d738a48b | as shown above, the construction made extensive use | as shown above, the construction made extensive use of metal; the forward fuselage was composed of steel; aft of the twin-seat cabin, monocoque wooden construction is present. the fully-glazed cabin is fully-integral with the fuselage; entry and egress is via sliding upper section. dual flight controls and comprehensiv... | wikipedia |
0d1c1127af6e966618b2d6459838ba2ed1dbadab | a trade paper advertisement by i.g. farben in | a trade paper advertisement by i.g. farben in may 1939 took advantage of the record-breaking flight from libya to india in late 1938 (see § operational history below) using the flight path as a background, and presented a breakdown of the materials used in the aircraft: wood 38.5%, elektron (cast lightweight magnesium-... | wikipedia |
475da8629e6f58c464b1971b08fa0345e7b827d5 | the ar 79 was a purpose-built touring and | the ar 79 was a purpose-built touring and trainer aircraft, possessing excellent flight characteristics through its use of modern aerodynamic innovations. through the use of split flaps, it could be flown at unusually slow speeds while, when correctly trimmed, stable hands-off flying could also be readily achieved. the... | wikipedia |
62ee5a9ef718eb9126a690394dead5eb8e65da03 | although it drew upon these earlier touring aircraft, | although it drew upon these earlier touring aircraft, the design team decided that this new aircraft, which would be designated ar 79, would be designed for greater reliability, ruggedness, and economy. to promote the aircraft to civil customers, arado committed to an extensive advertising campaign as a faster alternat... | wikipedia |
e145bef01335a0df9bd2eac368022e6dd190f98c | during the 1920s and early 1930s, the german | during the 1920s and early 1930s, the german aircraft manufacturer arado had entered into the touring aircraft sector with the arado l i and arado l ii. their designer, the aeronautical engineer walter rethel, sought to develop a more capable successor during the mid 1930s. it is likely that the decision to proceed was... | wikipedia |
e69dc14aca51860f0e75c613c993f1462960c546 | first flying in april 1938, the ar 79 | first flying in april 1938, the ar 79 promptly set multiple world speed records in their class that same year and was praised by high-ranking nazi officials. various german figured purchased individual aircraft, including ernst udet, hanna reitsch, heinz rühmann, alfried krupp von bohlen und halbach, and stephan von ho... | wikipedia |
2722fd0756acd692898383e63a04fc70833dd37d | the ar 79 was developed during the mid-1930s | the ar 79 was developed during the mid-1930s as a successor to the arado l i and arado l ii touring aircraft by the aeronautical engineer walter rethel. he designed a monoplane with a retractable tailwheel undercarriage that featured mixed construction, the forward fuselage was composed of fabric over steel tube while ... | wikipedia |
af0c35c809eecb2ff1057c7da4b8366502fc31c2 | anaa airport is an airport serving anaa, an | anaa airport is an airport serving anaa, an atoll in the tuamotu archipelago in french polynesia. it is located 2 kilometres (1.2 mi) southeast of the village of tukuhora. the airport type is medium and the world area code is 823. the nearest airport (76.22 km) is faaite airport. the airport is recorded to be 3m above ... | wikipedia |
2be9db5ba67525a2b1a9a1b21da3185270ebfefa | anaa airport (iata: aaa, icao: ntga) is an | anaa airport (iata: aaa, icao: ntga) is an airport serving anaa, an atoll in the tuamotu archipelago in french polynesia. it is located 2 kilometres (1.2 mi) southeast of the village of tukuhora. the airport type is medium and the world area code is 823. the nearest airport (76.22 km) is faaite airport. the airport is ... | wikipedia |
e5889de48e8df1ad9ced23335fd210795a3ec910 | the spectrum of a chirp pulse describes its | the spectrum of a chirp pulse describes its characteristics in terms of its frequency components. this frequency-domain representation is an alternative to the more familiar time-domain waveform, and the two versions are mathematically related by the fourier transform. the spectrum is of particular interest when pulses... | wikipedia |
f7363a63a48420f1a003d66bd182d408b508b953 | as examples, below are two plots of the | as examples, below are two plots of the spectral magnitudes of such chirps, with time-bandwidth products of 250 and 25, respectively. these chirps have reduced energy content in their outer frequency regions, but still show less than ideal performance. | wikipedia |
9ed583771a3878fdac852def9487fb73c73f49ae | t t = 1 2 + ω ω | t t = 1 2 + ω ω m a x + 0.1871 sin (2 π ω ω m a x) + 0.014895 sin (4 π ω ω m a x) {\displaystyle {\frac {t}{t}}={\frac {1}{2}}+{\frac {\omega }{\omega _{max}}}+0.1871\sin \left({\frac {2\pi \omega }{\omega _{max}}}\right)+0.014895\sin \left({\frac {4\pi \omega }{\omega _{max}}}\right)} rearranging the equation, one can... | wikipedia |
51a0dcb1be4c472d2209628ed5f7d120f435ef13 | non-linear chirps can be devised that have a | non-linear chirps can be devised that have a bell shaped spectrum, such as the blackman-harris window just discussed, and consequently will exhibit reduced ripple compared to the linear chirp. by means of the stationary phase method described earlier, an approximate relationship between time and frequency can be obtain... | wikipedia |
40f86ee5d393cc9f179d7859b104b12751a9adf8 | although spectral shaping of a chirp could be | although spectral shaping of a chirp could be applied in the frequency domain, better results are obtained if the shaping is carried out in the time domain. examples of this process are shown for linear chirps with time-bandwidth products of 250 and 25. they have been shaped by a 3-term blackman-harris window given by ... | wikipedia |
c5f28b2097f5c2521e6cb9389f6a9cf244882f96 | there are many applications in which a spectrum | there are many applications in which a spectrum with a rectangular magnitude profile is not ideal. for example, when a chirp waveform is compressed by means of its matched filter, then the resultant waveform approximates to the sinc function and, consequently, has annoyingly high sidelobes. often, to improve the charac... | wikipedia |
01c7d43347bc2d3eb459515ba42298b03beead76 | as an example, a linear chirp waveform with | as an example, a linear chirp waveform with a time bandwidth of 25 is shown together with its spectrum magnitude (shown by a full line) which, as demonstrated earlier, has a large ripple component. it is possible to find, by means of an inverse fft, a chirp waveform which, in the frequency domain, has the same phase ch... | wikipedia |
fc680d0751ce943dfc526b4e047aef9b67534e85 | this method uses an inverse fourier transform in | this method uses an inverse fourier transform in order to derive a waveform which has a spectrum with the phase characteristic of a chosen chirp but a new amplitude profile which is rectangular and ripple free. the method is very effective but, unfortunately, the waveform that is so derived has a semi-infinite time dur... | wikipedia |
8ea72a11efe1c76aec47243ac2a76d3f664eb3dc | the ripple reduction achieved by frequency pre-correction, although | the ripple reduction achieved by frequency pre-correction, although significant, is seen to be less successful than that achieved by the amplitude modulation methods of the previous section. however, it has been suggested that by implementing cubic (rather than quadratic) phase pre-correction, comparable results can be... | wikipedia |
cbaf92325f6a6d05e2795fa50404a5f8ebb3bcaf | in 1988, later work proposed slightly different values, | in 1988, later work proposed slightly different values, namely: Δ f p = 0.73 Δ f a n d δ = 0.86 / Δ f {\displaystyle \delta f_{p}=0.73\delta f\qquad and\qquad \delta =0.86/\delta f} | wikipedia |
e05df87df0910ab12fbc8df7edf6e30665c274d5 | this added distortion is referred to as 'predistortion'. | this added distortion is referred to as 'predistortion'. suggested values for these distortion regions, to achieve good results, were initially determined to be: Δ f p = 0.75 Δ f a n d δ = 1 / Δ f {\displaystyle \delta f_{p}=0.75\delta f\qquad and\qquad \delta =1/\delta f} | wikipedia |
8d0d002cef8d65dfababac9660ca3bbd289f34d9 | a analogous technique can be applied to the | a analogous technique can be applied to the frequency characteristic of the chirp waveform by adding linear fm distortion segments (quadratic phase modulation distortion) to the frequency characteristic of the chirp, as shown. the method is effective because amplitude and phase distortions having functional similarity ... | wikipedia |
e6bd3d3cf818573f369c15a6370ac63e0ba1ba1f | two examples show the spectra of linear chirps | two examples show the spectra of linear chirps with finite rise-times. the first is for a chirp with time-bandwidth of 250, where the rise and fall times are 4% of the total pulse duration and the second is for a chirp with time-bandwidth of 25, where the rise and fall times are 10% of the total. these two spectra show... | wikipedia |
d2802840913369cfb3f96ca7717d31a39ec3c9f8 | if the transitions at the start and end | if the transitions at the start and end of the chirp are made less sudden (or more 'rounded'), then a reduction in ripple amplitude is achieved. the durations of the two transition regions need only be a small fraction of the pulse duration, and suggested values are between 2/ Δ f and 3/ Δ f but, as expected, when the ... | wikipedia |
0e09add0086d2884ced5b8a6bad8afa606e06440 | although there are a number of procedures that | although there are a number of procedures that can be applied to reduce the ripple levels, they are not all equally effective. furthermore, some of the methods require amplitude shaping, or amplitude modulation, of the chirp pulse and this makes those methods unsuitable when, for example, the chirp pulses are to be tra... | wikipedia |
7534f412687e7ef43dcdc5eb25dd152313b594f5 | the fresnel ripples on a chirp spectrum are | the fresnel ripples on a chirp spectrum are very obtrusive, especially when time-bandwidth products are low (under 50, say) and their presence leads to high time sidelobe levels when chirps are subject to pulse compression as in radar and sonar systems. they arise because of the sudden discontinuities in the chirp wave... | wikipedia |
719ce4b396a92426a1bd187dc48ceae3787b981f | there is very little spectral content beyond the | there is very little spectral content beyond the sweep frequency range of a chirp pulse and this is especially true for waveforms where the time-bandwidth product is large. the full line on the graph of the adjacent figure shows results for linear chirps. it shows, for example, that only about 2% of the total power res... | wikipedia |
baf42493cd56ab87d639f1b71069dd2cdd2ea7a4 | to display the spectrum in more detail (but | to display the spectrum in more detail (but not necessarily with more resolution), the time sequence can be extended by zero padding. for example, extending the 128 point time sequence with zeros to give n = 4096 results in that part of the spectrum originally presented in 16 samples, now being presented in 512 samples... | wikipedia |
c6b59b362214197ff9e0b1d9dc1ee78a0653414c | by calculating the n-point fft of this data, | by calculating the n-point fft of this data, the discrete spectrum of the sequence is obtained. the magnitude of this spectrum is shown in the attached figure, where these data points are samples in frequency. the data is cyclic so, in the plot, the zero frequency point is at n = 0 and also at n = 128 (i.e. both points... | wikipedia |
6548c72695648572ba2ddd2eae1063bfc800f38f | the calculations can be carried out by means | the calculations can be carried out by means of a straightforward computer algorithm, but this is not very efficient in computer usage. consequently, more efficient algorithms have been developed, especially fast fourier transforms (fft). computer programs which implement the fft are widely available in the literature ... | wikipedia |
8849053a0651702afa7aeb71082e51121ca92ca6 | s s m = s s (j 2 | s s m = s s (j 2 π m n w) = ∑ n = 0 n − 1 s n ⋅ e x p (− j (2 π m n n) {\displaystyle ss_{m}\quad =ss\left(j{\frac {2\pi m}{nw}}\right)\quad =\quad \sum _{n=0}^{n-1}s_{n}\cdot exp(-j\left({\frac {2\pi mn}{n}}\right)} | wikipedia |
28a9b79d9708392c6df68ebf7ee3a87581202a4b | if we limit interest in the output spectrum | if we limit interest in the output spectrum to a finite number of discrete data points (= n), at frequencies ω given by ω m = 2 π m n w f o r m = 0, 1, 2,... n − 1 {\displaystyle \omega _{m}={\frac {2\pi m}{nw}}\qquad for\qquad m=0,1,2,...n-1} | wikipedia |
8d7a35836c653d1d87d8628b46055049cdc74dbd | although the characteristic of the zero order hold | although the characteristic of the zero order hold has a small influence on this result, the slope is mainly due to the properties of the chirp. the waveform sweeps relatively quickly over the high frequencies and spends more time sweeping the low frequencies, consequently there is less energy content at the high frequ... | wikipedia |
701a5f055b900e4156ca093f76003f441e7fde38 | the sampled spectrum, ss(ω) of this waveform, calculated | the sampled spectrum, ss(ω) of this waveform, calculated using the equation given above, is shown. to simplify the plot, only the results at positive frequencies have been displayed. the influence of the frequency spectrum of the zero order hold circuit is clearly seen in the diagram. | wikipedia |
3bd9848114e26c40168aa6ccd34e484da090512c | the second term in the equation is called | the second term in the equation is called the fourier transform of the discrete signal s. it is a continuous function over all ω and involves an infinite number of summations. in practice the summation process can be truncated to a finite number of samples, n, possibly because the waveform is periodic or zero outside t... | wikipedia |
4e5c5e4b3cca42a6d75ad5b6df37f316c262371f | the first part of the expression, i.e. the | the first part of the expression, i.e. the 'sin(x)/x' part, is the frequency response of the sample and hold. its amplitude decreases with frequency and it falls to 63% of its peak value at half the sampling frequency and it is zero at multiples of that frequency (since f =1/w). | wikipedia |
37e38a55d34c24eb91afca52ef99c8a9e37c0c90 | s s (ω)) = w sin (ω w | s s (ω)) = w sin (ω w / 2) ω w / 2 ⋅ {\displaystyle ss(\omega))=w{\frac {\sin(\omega w/2)}{\omega w/2}}\cdot \left} | wikipedia |
f1eb0e0324f021c20ba107ba20442caffe096ae0 | the result so obtained is the convolution of | the result so obtained is the convolution of a rectangular pulse with step size w with the impulses located at the sampling instants with weights equal to the sample values. in consequence, the spectrum of interest will have superimposed upon it the frequency response of the sample and hold, and the spectrum of the sam... | wikipedia |
fe8493622f222c492c157de92e833f5801f0711f | a straightforward way to approximate an integral, such | a straightforward way to approximate an integral, such as a fourier integral, is to use the standard ' rectangle rule ' for numerical integration. the method assumes the signal value taken at a sample instant remains constant for one sampling interval, until the next sample is taken. this procedure is sometimes referre... | wikipedia |
600b1b278a8bc4eb77b765cd500b2aad7fb5918f | one consequence of sampling is that the resultant | one consequence of sampling is that the resultant spectrum is periodic in the frequency domain. in addition to the (desired) baseband spectrum, additional versions of the spectrum occur, centered on multiples of the sampling frequency. to ensure that there is no overlapping of frequency data (i.e. no aliasing) the nyqu... | wikipedia |
4b5199d6a0c011215b9bc9c44ff0d3d83d2f4f2e | the stationary phase method does not predict or | the stationary phase method does not predict or deal with fresnell ripples, so it is unable to offer any means by which these ripples can be minimized. as an example, the figure below shows a chirp spectrum with t. Δ f =250 obtained for a non-linear chirp aiming to match the hamming window, using the methods described ... | wikipedia |
d9f1c25fdf2e7fc81af7d95ea6a90b7e593d70b5 | t t = 1 2 + ω ω | t t = 1 2 + ω ω m a x + 1.7037 4 π ⋅ s i n (2 π ω ω m a x) {\displaystyle {\frac {t}{t}}={\frac {1}{2}}+{\frac {\omega }{\omega _{max}}}+{\frac {1.7037}{4\pi }}\cdot sin\left({\frac {2\pi \omega }{\omega _{max}}}\right)} | wikipedia |
bbdc6eeb30e013c4e4454593ec710545d2f0d480 | it is possible to find the group delay | it is possible to find the group delay characteristics of these functions in a similar manner to that carried out above and the results for n = 1 to 4 have been calculated. although these cosine functions are amenable to mathematical manipulation, they are rarely chosen to define the spectral characteristics of a chirp... | wikipedia |
699d300a8d0edf16591f7a9a826e51379818a31c | | s (ω) | 2 = a n | | s (ω) | 2 = a n ⋅ c o s n (π ω ω m a x) w h e r e | ω | < ω m a x 2 a n d n i s a n i n t e g e r {\displaystyle |s(\omega)|^{2}=a_{n}\cdot cos^{n}\left({\frac {\pi \omega }{\omega _{max}}}\right)\qquad where\qquad |\omega |<{\frac {\omega _{max}}{2}}\qquad and\ n\ is\ an\ integer} | wikipedia |
1ea291f9bef339be127b6c6a80dd249c6420fbfe | the linear chirp is just one special case | the linear chirp is just one special case which, in any case, can be calculated more precisely by the methods of the earlier section. the particular usefulness of the stationary phase method lies in its ability to provide results when the frequency sweep is non linear. in such cases the spectral response can be shaped ... | wikipedia |
5e61a34cddc0602bb9ada6109a86f45312d891c9 | put d(- ω /2) = 0 and d(ω | put d(- ω /2) = 0 and d(ω /2) = t, where t is the pulse duration, then k = t/2 and a = (2 π t)/ ω so, finally d (ω) = t ⋅ {\displaystyle d(\omega)=t\cdot \left} | wikipedia |
5518c0ce9e0a95e3efe7d3886503d7177bff41c6 | | s (ω) | 2 = a f | | s (ω) | 2 = a f o r | ω | < ω m a x 2 {\displaystyle |s(\omega)|^{2}=a\qquad for\qquad |\omega |<{\frac {\omega _{max}}{2}}} so d (ω) = 1 2 π ⋅ ∫ a ⋅ d ω + k = a 2 π ⋅ ω + k {\displaystyle d(\omega)={\frac {1}{2\pi }}\cdot \int a\cdot d\omega +k={\frac {a}{2\pi }}\cdot \omega +k} | wikipedia |
3b176440b941b558ef6a90484816fbbcadf9746f | so in the case of a rectangular time | so in the case of a rectangular time envelope, the dispersive delay characteristic is given by the integral of the square of the envelope. if the positive sign is taken, then the group delay increases with increasing frequency and vice versa. the result is only approximate, but is more accurate for large values of the ... | wikipedia |
a64dc1dc9b092b321ecb41f776e41d389d71a468 | d (ω) = − Φ ′ (ω) = | d (ω) = − Φ ′ (ω) = − ∫ 0 ∞ Φ ″ (ω) ⋅ d ω + k {\displaystyle d(\omega)=-\phi '(\omega)=-\int _{0}^{\infty }\phi ''(\omega)\cdot d\omega +k} so d (ω) = ± 1 2 π ⋅ ∫ 0 ∞ | s (ω) | 2 ⋅ d ω + k {\displaystyle d(\omega)=\pm {\frac {1}{2\pi }}\cdot \int _{0}^{\infty }|s(\omega)|^{2}\cdot d\omega +k} | wikipedia |
9b5be07ffe228a2f5d3078ea920dfed4a4eb247e | there are two solutions for Φ (ω), which | there are two solutions for Φ (ω), which are complex conjugates of each other. the two filters with these characteristics can be used as the transmitter and receiver filters of a radar system and are interchangeable. the group delay characteristic d(ω), (where d(ω)=-d Φ /d ω), is | wikipedia |
da4b6b5581847ab43b2c5bf76cc0c43e09942350 | Φ ″ (ω) = ± 1 2 π | Φ ″ (ω) = ± 1 2 π ⋅ | s (ω) | 2 {\displaystyle \phi ''(\omega)=\pm {\frac {1}{2\pi }}\cdot |s(\omega)|^{2}} | wikipedia |
19c9e53f12d5c6a3cf3ab45247f55d3d9f31d632 | although the relationships are only approximate, their accuracy | although the relationships are only approximate, their accuracy improves as the time-bandwidth product increases. in cases where the signal envelope and spectrum modulus are defined by smoothly varying gaussian function then a t. Δ f product as low as 15 will give acceptable results, but if both a(t) and |s(ω)| are def... | wikipedia |
62c902d92f2bf11a2a6838dee9a6fe6b843dc786 | consequently, approximate expressions for a(t) and θ (t) | consequently, approximate expressions for a(t) and θ (t) can be obtained when the spectrum, including its phase function Φ (ω) is given and, similarly, approximate expressions for |s(ω | and Φ (ω) can be obtained when the signal characteristics are given. several examples of the procedure are given in the literature | wikipedia |
51030d2180e6f9ac595c544b0f09b28fb148fe94 | in effect, stationary phase analysis gives the following | in effect, stationary phase analysis gives the following (approximate) fourier pair relationships: a (t) ⋅ exp ≊ 1 2 π ⋅ ∫ − ∞ ∞ s (ω) | ⋅ exp ⋅ d ω {\displaystyle a(t)\cdot \exp\approxeq {\frac {1}{2\pi }}\cdot \int _{-\infty }^{\infty }s(\omega)|\cdot \exp\cdot d\omega } and | s (ω) | ⋅ exp ≊ ∫ − ∞ ∞ a (t) ⋅ exp d t ... | wikipedia |
4e98111d07f31e16a96dd0cc36120902a7bdd389 | a 2 (t ω) ≊ 1 2 π | a 2 (t ω) ≊ 1 2 π ⋅ | s (ω) | 2 | Φ ″ (ω) | {\displaystyle a^{2}(t_{\omega })\approxeq {\frac {1}{2\pi }}\cdot {\frac {|s(\omega)|^{2}}{|\phi ''(\omega)|}}} | wikipedia |
a41106825fe7afa28bfd6f50a1a51c36a8ad84ba | s (t) = 1 2 π ∫ − | s (t) = 1 2 π ∫ − ∞ ∞ | s (ω) | ⋅ exp ⋅ d ω {\displaystyle s(t)={\frac {1}{2\pi }}\int _{-\infty }^{\infty }|s(\omega)|\cdot \exp\cdot d\omega } | wikipedia |
8f60f286908c08b4c570ef2858857bc0ba2a65ba | in this equation t represents a constant time | in this equation t represents a constant time point, so terms depending on t alone may be taken outside the integral. the expression simplifies to s (ω) ≊ 2 π ⋅ a (t s) | θ ″ (t) | ⋅ exp {\displaystyle s(\omega)\approxeq {\sqrt {2\pi }}\cdot {\frac {a(t_{s})}{\sqrt {|\theta ''(t)|}}}\cdot \exp \left} so | s (ω t) | 2 ≊... | wikipedia |
bd3e205cc7df9f61a39af76aa16e00b3098813c5 | s (ω) ≊ a (t s) ∫ t | s (ω) ≊ a (t s) ∫ t s − δ t s + δ exp ⋅ d t {\displaystyle s(\omega)\approxeq a(t_{s})\int _{t_{s}-\delta }^{t_{s}+\delta }\exp \left\cdot dt} | wikipedia |
3013a909932594376351ab8bda66f081ce29c1d2 | unless θ (t) is a constant, the point | unless θ (t) is a constant, the point in time t at which the phase is stationary will vary according to the instantaneous frequency ω. expressing the difference between (ω - ω).t and θ (t) as a taylor series about the time t, but discarding all but the first three terms (of which the second term is zero, here), the fou... | wikipedia |
06ea90eed157a03e962dac0befbfb7e355f474a6 | d d t = 0 o r (ω | d d t = 0 o r (ω − ω 0) − θ ′ (t) = 0 {\displaystyle {\frac {d}{dt}}=0\qquad or\qquad (\omega -\omega _{0})-\theta '(t)=0} | wikipedia |
48b0b6615fd29d89c714f84a20f5f20e1c10b460 | often (as in radar applications) a(t) is a | often (as in radar applications) a(t) is a slowly varying function of time and the phase θ (t) is oscillatory and varies rapidly, over the range of integration. with such waveforms, the stationary phase approximation can be used to investigate the spectrum. the method relies on the fact that the major contributions to ... | wikipedia |
9b1218fef1fea972a78cbb17c1b2cedb51290680 | the residual phase term adds only minor perturbations | the residual phase term adds only minor perturbations to this characteristic within the frequency range Δ Ω ± Δ Ω / 2 {\displaystyle \delta \omega \pm \delta \omega /2}. at frequencies outside this range, Φ 2(ω) deviates rapidly from π /4, and so the total phase will deviate seriously from a square law there. fortunate... | wikipedia |
654b948f3564c37d9416f437f861f39a8f9c83b4 | consequently, for frequencies within the sweep range of | consequently, for frequencies within the sweep range of the chirp, it is the square-law phase term Φ 1(ω) and its group delay function (= -d Φ 1/d(ω)) that are of most interest. there is a plot of the group delay shown below. both this function and the phase Φ 1(ω) are independent of the value of the time-bandwidth pro... | wikipedia |
7e5d784bb63b6ed371426cfd348f0dcefc77a97a | in the case of the plots of residual | in the case of the plots of residual phase, Φ 2(ω), the profiles tend to be very similar over a wide range of time-bandwidth products. two examples, for txb = 100 and 250 are shown below. they have a phase angle close to a value of π /4 within the chirp range ω 0 ± Δ Ω / 2 {\displaystyle \omega _{0}\pm \delta \omega /2... | wikipedia |
b950c6e29bc3485935bc81c2db06b570c560fafc | some plots of the power spectrum |s(ω)| as | some plots of the power spectrum |s(ω)| as a function of frequency are shown, for time-bandwidth products of 25, 100, 250 and 1000. when the product is small, the fresnel ripples are very much in evidence, but the spectrum does tend to a more rectangular profile for larger values. | wikipedia |
a7304194707d9e9eaa532588111dbbb615f35626 | tables of the fresnel integrals have been published, | tables of the fresnel integrals have been published, together with mathematical routines with which to compute the integrals manually or by means of a computer program. in addition, a number of mathematical software programs, such as mathcad, matlab and mathematica have built-in routines to evaluate the integrals, eith... | wikipedia |
5fe924f9e84ddfd3884b3ae436514eac507fa680 | the ratio {\displaystyle \left} is approximately unity over | the ratio {\displaystyle \left} is approximately unity over a large part of frequency range of interest so Φ approximates to a constant phase angle π /4 there.if a frequency scaling term n is introduced, where n = 2 ⋅ (ω − ω 0) Δ Ω {\displaystyle n=2\cdot {\frac {(\omega -\omega _{0})}{\delta \omega }}}, then the expre... | wikipedia |
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