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°
Homework Answers
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Determine if the signal is periodic (4 points each) and plot
the Fourier series coefficients if...
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...
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. [10 Marks] Determine the Fourier series coefficients of the following signal, which is periodic in...
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
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]
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
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series ...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
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
2.10-3 Using direct integration, numerically derive and plot the exponential Fourier series coefficients of the followi...
2.10-3 Using direct integration, numerically derive and plot the exponential Fourier series coefficients of the following periodic signals: (a) The signal waveform of Figure P2.1-5 (b) The signal waveform of Figure P2.1-10(a) (c) The signal waveform of Figure P2.1-10(f) 2.10-4 Using the FFT method, repeat Problem 2.10-3. e P2.1-5 g (t) -6 4 -8
2.10-3 Using direct integration, numerically derive and plot the exponential Fourier series coefficients of the following periodic signals: (a) The signal waveform of Figure P2.1-5 (b)...
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)
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...
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. [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
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]
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
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
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
2.10-3 Using direct integration, numerically derive and plot the exponential Fourier series coefficients of the following periodic signals: (a) The signal waveform of Figure P2.1-5 (b) The signal waveform of Figure P2.1-10(a) (c) The signal waveform of Figure P2.1-10(f) 2.10-4 Using the FFT method, repeat Problem 2.10-3. e P2.1-5 g (t) -6 4 -8
2.10-3 Using direct integration, numerically derive and plot the exponential Fourier series coefficients of the following periodic signals: (a) The signal waveform of Figure P2.1-5 (b)...
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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