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10. The magnitude of the frequency spectrum of a signal X() is given below. The 6...
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency resp...
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency response: H(G What signal y(t) is observed at the output? Problem 2 The inverse Fourier transform of a system frequency response is given by h(t)t. The signal x(t) 3 cos(4t 0.5) is input to the system (t in seconds). (a) What is the expression of the signal y(t) at the system output? (b) What is the power attenuation in dB caused by the...
Sketch the frequency spectrum of he following signal and indicate the complex magnitude of each. All...
Sketch the frequency spectrum of he following signal and
indicate the complex magnitude of each. All amplitudes must be
positive
Determine fundamental frequency and period
*all phases need to be written in terms of pi between
-pi and pi.
Sketch the frequency spectrum of the following signal and indicate the complex magnitude of each frequency component Manipulate phase as necessary to plot all components of the spectrum with positive amplitudes: x(t) = 14 cos( 1 60mt-π/4) + 5 cos(280mt-2π/3) -cos(600πt...
5. Consider the following message signal: m(t) -2 .3 10 Assume that the carrier frequency is f ar...
5. Consider the following message signal: m(t) -2 .3 10 Assume that the carrier frequency is f are kf = 105, kp-25 respectively. 108 Hz, and frequency and phase deviation constants Find the maximum and minimum frequency deviation for FM, and sketch the FM wave for a duration of 103 seconds shown in the above figure (5 points). a. b. Find the maximum and minimum frequency deviation for PM, sketch the PM wave for a duration of 103 seconds shown...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal ; c. Determine the frequency/frequencies of aliasing noise . Q2)...
3. The following is the amplitude spectrum of a DSB+carrier AM signal x(f) 1.5 1.5 1.5 1.5 f (Hz)...
3. The following is the amplitude spectrum of a DSB+carrier AM signal x(f) 1.5 1.5 1.5 1.5 f (Hz) 1920 2000 2080 2080 2000 1920 (a) (10 points) Determine the carrier frequency fe the carrier amplitude Ac the mod ulation index ,, and the message signal m(t) of the AM signal. (b) (10 points) Given that μ2Sm 0.18, find the output SNR (in dB) if the received signal includes white noise with a power spectral density of η/2-10-10 W/Hz. (c)...
a. For the wideband FM signal given by SFM(t) = cos[2πfct+ 3sin2π25t]
a. For the wideband FM signal given by SFM(t) = cos[2πfct+ 3sin2π25t], draw only positive side of the spectrum, (from n=-5 to n=+5). Assume the carrier frequency (fc) of 1 KHz. Hint: First calculate β by comparing the signal with SFM(t) equation b. The FM signal of part (a) is passed through a bandpass filter centered at 1 KHz with a bandwidth of 210 Hz, as shown below. Draw the new spectrum and calculate the bandwidth and power of the filtered FM...
Consider a speech signal x() that has the following frequency spectrum: xga) 1 + cos( -/100 a) Se...
Digital Signal Processing
DFT
Consider a speech signal x() that has the following frequency spectrum: xga) 1 + cos( -/100 a) Select appropriate values of N and T that will help us carry out DFT-based spectral analysis of this signal x401@) 800 such that the continuous-time frequencies are sampled no farther than 10 Hz apart. b) Ignore the issue of spectral leakage; under this assumption, provide a closed-form expression for the DFT of the signal using the values selected in...
Problem 1 (10 pts). A time-domain signal x(t) is given in the figure below: - -...
Problem 1 (10 pts). A time-domain signal x(t) is given in the figure below: - - - - - - - 9 X(t) 0 2 t, msec (a) Compute the simplest real-valued math function for the spectrum X($). (b) Plot X(f) over a Hz frequency range large enough to show all the important properties.
Given an energy signal x(t) = (t-5T)e-t-T) , where T-0.1 compute its energy spectrum density in...
Given an energy signal x(t) = (t-5T)e-t-T) , where T-0.1 compute its energy spectrum density in Matlab 1. use two different methods to a. Get its spectrum using Fourier transformation, follovfed by the squaring its amplitude. Plot its Fourier transformation and its energy spectrum density. Get its autocorrelation function, followed by its Fourier transformation. Plot its autocorrelation function and its energy spectrum density. b. 2. In a multipath channel, the received signal y (t) x(t) 0.15x(t -6T) +0.09x(t 10.5T), plot...
2. [20 points] The carrier c(t-Acce(2106 t) is frequency modulated by the sinusoid signal m(t) 2cos...
2. [20 points] The carrier c(t-Acce(2106 t) is frequency modulated by the sinusoid signal m(t) 2cos (2000mt). The deviation constant is kr 3000 Hz/V Determine the bandwidth of the modulated signal using Carson's rule a. Sketch the magnitude of the spectrum of the modulated signal (plot only those frequency components that lie within the bandwidth derived in part a) with detailed information such as the areas of delta function determined by the Bessel function, frequency separation between each spectrum (note...
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency response: H(G What signal y(t) is observed at the output? Problem 2 The inverse Fourier transform of a system frequency response is given by h(t)t. The signal x(t) 3 cos(4t 0.5) is input to the system (t in seconds). (a) What is the expression of the signal y(t) at the system output? (b) What is the power attenuation in dB caused by the...
Sketch the frequency spectrum of he following signal and
indicate the complex magnitude of each. All amplitudes must be
positive
Determine fundamental frequency and period
*all phases need to be written in terms of pi between
-pi and pi.
Sketch the frequency spectrum of the following signal and indicate the complex magnitude of each frequency component Manipulate phase as necessary to plot all components of the spectrum with positive amplitudes: x(t) = 14 cos( 1 60mt-π/4) + 5 cos(280mt-2π/3) -cos(600πt...
5. Consider the following message signal: m(t) -2 .3 10 Assume that the carrier frequency is f are kf = 105, kp-25 respectively. 108 Hz, and frequency and phase deviation constants Find the maximum and minimum frequency deviation for FM, and sketch the FM wave for a duration of 103 seconds shown in the above figure (5 points). a. b. Find the maximum and minimum frequency deviation for PM, sketch the PM wave for a duration of 103 seconds shown...
3. The following is the amplitude spectrum of a DSB+carrier AM signal x(f) 1.5 1.5 1.5 1.5 f (Hz) 1920 2000 2080 2080 2000 1920 (a) (10 points) Determine the carrier frequency fe the carrier amplitude Ac the mod ulation index ,, and the message signal m(t) of the AM signal. (b) (10 points) Given that μ2Sm 0.18, find the output SNR (in dB) if the received signal includes white noise with a power spectral density of η/2-10-10 W/Hz. (c)...
Digital Signal Processing
DFT
Consider a speech signal x() that has the following frequency spectrum: xga) 1 + cos( -/100 a) Select appropriate values of N and T that will help us carry out DFT-based spectral analysis of this signal x401@) 800 such that the continuous-time frequencies are sampled no farther than 10 Hz apart. b) Ignore the issue of spectral leakage; under this assumption, provide a closed-form expression for the DFT of the signal using the values selected in...
Problem 1 (10 pts). A time-domain signal x(t) is given in the figure below: - - - - - - - 9 X(t) 0 2 t, msec (a) Compute the simplest real-valued math function for the spectrum X($). (b) Plot X(f) over a Hz frequency range large enough to show all the important properties.
Given an energy signal x(t) = (t-5T)e-t-T) , where T-0.1 compute its energy spectrum density in Matlab 1. use two different methods to a. Get its spectrum using Fourier transformation, follovfed by the squaring its amplitude. Plot its Fourier transformation and its energy spectrum density. Get its autocorrelation function, followed by its Fourier transformation. Plot its autocorrelation function and its energy spectrum density. b. 2. In a multipath channel, the received signal y (t) x(t) 0.15x(t -6T) +0.09x(t 10.5T), plot...
2. [20 points] The carrier c(t-Acce(2106 t) is frequency modulated by the sinusoid signal m(t) 2cos (2000mt). The deviation constant is kr 3000 Hz/V Determine the bandwidth of the modulated signal using Carson's rule a. Sketch the magnitude of the spectrum of the modulated signal (plot only those frequency components that lie within the bandwidth derived in part a) with detailed information such as the areas of delta function determined by the Bessel function, frequency separation between each spectrum (note...
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