![1. [10 Marks] Determine the Fourier series coefficients of the following signal, which is periodic in T 10. 10 -3-1 1 3 10 2. 10 Marks] Determine the Fourier transform of the following signal, which is zero outside the indicated range. -3-1 1 3](http://img.homeworklib.com/questions/05782d30-c0ac-11eb-83b5-8f4912fa2f15.png?x-oss-process=image/resize,w_560)
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1. [10 Marks] Determine the Fourier series coefficients of the following signal, which is periodic in...
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)
Find the Fourier series representation of the following periodic signal. The expressions for the coefficients, Dn,...
Find the Fourier series representation of the following periodic
signal. The expressions for the coefficients, Dn, and for the
Fourier series representation of x(t) must not contain complex
expressions (combine complex exponentials into sinusoids).
3 2.5 exp(t/2 1.5 0.5 -4
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0,...
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.
Determine if the signal is periodic (4 points each) and plot the Fourier series coefficients if...
Determine if the signal is periodic (4 points each) and plot the Fourier series coefficients if the signal is periodic. (16 points) xt=3cos10πt+2cos25t xt=3+8cos8πt+2cos12πt+40°
2.For the periodic DT signal shown in Top, a) determine the Fourier Series Coefficients. b) Use...
2.For the periodic DT signal shown in Top, a) determine the
Fourier Series Coefficients. b) Use MATLAB to generate a spectral
plot (magnitude plot and a separate phase plot). c) Use MATLAB to
generate and plot the signal as a DTFS expansion of the periodic
signal. Plot over an interval containing several periods. Make sure
to include the MATLAB code
x[ri] -9 63 3 9 12 n 1. For the periodic DT signal shown in Top, a) determine the Fourier...
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]
Question 3 Determine the Exponential Fourier Series of the periodic signal shown in Figure 1 F(t)...
Question 3 Determine the Exponential Fourier Series of the periodic signal shown in Figure 1 F(t) 1 -2 1 2 Figure 1 (10 marks)
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)
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal...
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal x[n]. i. ii. [5] Use Parseval's relation to determine the average power of x[n]. [5] Let bx be the Fourier series coefficients of a DT signal y[n). Without computing x[n], determine bk in terms of ak if y[n] is related to x[n] by y[n] = ejinx[n] Plot bk for k=0,1,2, ... 7. ak 16
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]....
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]. (Hints: find shortcuts using trigonometric formulas, and note that c can be obtained from a) and b).) rom a an a)() 10t) b) g(t)+cos(2t) c) f(t)1cos(2t) sin(10T) cos(2 sin
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)
Find the Fourier series representation of the following periodic
signal. The expressions for the coefficients, Dn, and for the
Fourier series representation of x(t) must not contain complex
expressions (combine complex exponentials into sinusoids).
3 2.5 exp(t/2 1.5 0.5 -4
6) If a continuous-time periodic signal has the Fourier series coefficients ak, where k = 0, +1, +2, +3,..., derive the Fourier series coefficients bk of the following signals in terms of aki a) <(-t) b) x*(t) c) x(t – t.) where t, is a constant e) (t) dt In part e), assume that the average value of x(t) is zero.
2.For the periodic DT signal shown in Top, a) determine the
Fourier Series Coefficients. b) Use MATLAB to generate a spectral
plot (magnitude plot and a separate phase plot). c) Use MATLAB to
generate and plot the signal as a DTFS expansion of the periodic
signal. Plot over an interval containing several periods. Make sure
to include the MATLAB code
x[ri] -9 63 3 9 12 n 1. For the periodic DT signal shown in Top, a) determine the Fourier...
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]
Question 3 Determine the Exponential Fourier Series of the periodic signal shown in Figure 1 F(t) 1 -2 1 2 Figure 1 (10 marks)
I) The following signal xcn is periodic th Period NFind the Fourier Series coefficients of the Signal nJ, cos (AT n+2)
d) [10] The figure below shows the Fourier series coefficients ak of the DT periodic signal x[n]. i. ii. [5] Use Parseval's relation to determine the average power of x[n]. [5] Let bx be the Fourier series coefficients of a DT signal y[n). Without computing x[n], determine bk in terms of ak if y[n] is related to x[n] by y[n] = ejinx[n] Plot bk for k=0,1,2, ... 7. ak 16
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]. (Hints: find shortcuts using trigonometric formulas, and note that c can be obtained from a) and b).) rom a an a)() 10t) b) g(t)+cos(2t) c) f(t)1cos(2t) sin(10T) cos(2 sin
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