Given the periodic signal ?(?)=H0,−1<?<0 2−2?,0<?<1 with a signal period of 2 sec. Obtain the Fourier...
Given the periodic signal ?(?)=H0,−1<?<0 2−2?,0<?<1
with a signal period of 2 sec. Obtain the Fourier series
coefficients using the Fourier sine and Fourier cosine series
expansions.
Homework Answers
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Given the periodic signal ?(?)=H0,−1<?<0 2−2?,0<?<1
with a signal period of 2 sec. Obtain the Fourier...
Consider an arbitrary periodic signal with a period of 2 seconds. Give the equation for the...
Consider an arbitrary periodic signal with a period of 2 seconds. Give the equation for the infinite Fourier Series (Trigonometric Form) for this signal. k-1 where, the fundamental period/frequency is: TO = 2 sec and fo a) List the frequencies present in the analog (continuous-time) signal b) Assume that the analog sig alissa pled at 2 H List the dig a f equences present in the resulting digital signal. c) What are the magnitudes of the sine and cosine terms...
3.59. (a) Suppose x[n] is a periodic signal with period N. Show that the Fourier series coefficie...
please
3.59. (a) Suppose x[n] is a periodic signal with period N. Show that the Fourier series coefficients of the periodic signal are periodic with period N. (b) Suppose that x() is a periodic signal with period T and Fourier series coeffi cients a with period N. Show that there must exist a periodic sequence g[n] such that (c) Can a continuous periodic signal have periodic Fourier coefficients?
3.59. (a) Suppose x[n] is a periodic signal with period N. Show...
Consider an arbitrary periodic signal with a period of 2 seconds. Give the equation for the...
Consider an arbitrary periodic signal with a period of 2
seconds.
Give the equation for the infinite Fourier Series (Trigonometric
Form) for this signal.
where, the fundamental period/frequency is:
=2
sec and
=12 Hz
a)List the frequencies present in the analog (continuous-time)
signal.
b)Assume that the analog signal is sampled at 2 Hz. List the
digital frequencies present in the resulting digital signal.
c)What are the magnitudes of the sine and cosine terms
associated with each of these digital frequencies?...
For the periodic signal below, find the compact trigonometric fourier series and sketch the amplitude and...
For the periodic signal below, find the compact trigonometric
fourier series and sketch the amplitude and phase spectra. If
either the sine or cosine terms are absent in the Fourier series,
explain why. Please provide a detailed solution. Thanks!
For the periodi the amplitude and phase spectra. If either the sine or cosine terms a series, explain why 6.1-1. c signal shown below, find the compact trigonometric Fourier series and sketch re absent in the Fourier b) -20
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass...
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass through an ideal lowpass filter with cut off frequency =102.5Hz. The resulting signal y, (t) is sampled periodically with T 0.005 sec determine the spectrum of the sequence y(n) = ya(nT)
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients...
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients ak, show that if r(t) is even, then its Fourier series coefficients must be real and even. [10 points]
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t...
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t s To. To2 and x(t)-0 a) Plot x(t) b) Expand x(t) in trigonometric Fourier series (sine/cosine). c) Calculate the average power of x().
The Fourier series of a periodic signal s(2) of period T can be expressed as k...
The Fourier series of a periodic signal s(2) of period T can be expressed as k s(x) = cxexp ( 21 - where the coefficients Ck are given by 7/2 CR 1 T -T/2 | $(z) exp (-27 k -27=cdc T (i) Consider s(2) of period T = 6 and amplitude A= 2: 8(z) = 2 * |< T 2 Compute the Fourier coefficients ok. (ii) Use the identities exp(Trik) + exp(-rik) cos(Tk) = 2 sin(Tk) exp(Trik) – exp(-rik) 2i...
I) The following signal xcn is periodic th Period NFind the Fourier Series coefficients of the...
I) The following signal xcn is periodic th Period NFind the Fourier Series coefficients of the Signal nJ, cos (AT n+2)
Consider an arbitrary periodic signal with a period of 2 seconds. Give the equation for the infinite Fourier Series (Trigonometric Form) for this signal. k-1 where, the fundamental period/frequency is: TO = 2 sec and fo a) List the frequencies present in the analog (continuous-time) signal b) Assume that the analog sig alissa pled at 2 H List the dig a f equences present in the resulting digital signal. c) What are the magnitudes of the sine and cosine terms...
please
3.59. (a) Suppose x[n] is a periodic signal with period N. Show that the Fourier series coefficients of the periodic signal are periodic with period N. (b) Suppose that x() is a periodic signal with period T and Fourier series coeffi cients a with period N. Show that there must exist a periodic sequence g[n] such that (c) Can a continuous periodic signal have periodic Fourier coefficients?
3.59. (a) Suppose x[n] is a periodic signal with period N. Show...
Consider an arbitrary periodic signal with a period of 2
seconds.
Give the equation for the infinite Fourier Series (Trigonometric
Form) for this signal.
where, the fundamental period/frequency is:
=2
sec and
=12 Hz
a)List the frequencies present in the analog (continuous-time)
signal.
b)Assume that the analog signal is sampled at 2 Hz. List the
digital frequencies present in the resulting digital signal.
c)What are the magnitudes of the sine and cosine terms
associated with each of these digital frequencies?...
For the periodic signal below, find the compact trigonometric
fourier series and sketch the amplitude and phase spectra. If
either the sine or cosine terms are absent in the Fourier series,
explain why. Please provide a detailed solution. Thanks!
For the periodi the amplitude and phase spectra. If either the sine or cosine terms a series, explain why 6.1-1. c signal shown below, find the compact trigonometric Fourier series and sketch re absent in the Fourier b) -20
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass through an ideal lowpass filter with cut off frequency =102.5Hz. The resulting signal y, (t) is sampled periodically with T 0.005 sec determine the spectrum of the sequence y(n) = ya(nT)
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients ak, show that if r(t) is even, then its Fourier series coefficients must be real and even. [10 points]
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t s To. To2 and x(t)-0 a) Plot x(t) b) Expand x(t) in trigonometric Fourier series (sine/cosine). c) Calculate the average power of x().
The Fourier series of a periodic signal s(2) of period T can be expressed as k s(x) = cxexp ( 21 - where the coefficients Ck are given by 7/2 CR 1 T -T/2 | $(z) exp (-27 k -27=cdc T (i) Consider s(2) of period T = 6 and amplitude A= 2: 8(z) = 2 * |< T 2 Compute the Fourier coefficients ok. (ii) Use the identities exp(Trik) + exp(-rik) cos(Tk) = 2 sin(Tk) exp(Trik) – exp(-rik) 2i...
I) The following signal xcn is periodic th Period NFind the Fourier Series coefficients of the Signal nJ, cos (AT n+2)
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