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1. (15) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth...
please show steps, focus on part b more 1. (23 points) Sampling and Aliasing. (a) Find...
please show steps, focus on part b more
1. (23 points) Sampling and Aliasing. (a) Find the Nyquist sampling rate wn for the given x(t). (Recall that the sampling frequency has to be twice larger than the bandwidth of the signal to recover the signal without loss of information.) i. (5 pts) X(t) = sinc(5000) * cos(7t). ii. (5 pts) r(t) = sin(101) cos(106) iii. (5 pts) (t) = sinc(50000) + cos(56) (b) (8 pts) Let r(t) = sinc(t/h), y(t)...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the sampled signal if the sampling rate is 25% higher than the Nyquist rate. a.) ft)sinc E 2T 10 b.) h)=sinc 2T For all the following, use ft) given in part a.) c.) glt)= f(l-7) d.) c(t)- f)cos() 1 e.) x(t)= fit)+ _ sinc (t
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the...
19. 1 mark) What is the Nyquist sampling rate for a band-pass signal with a bandwidth...
19. 1 mark) What is the Nyquist sampling rate for a band-pass signal with a bandwidth of 300kHz if the lowest frequency is 100kHz? 20. 1 mark) In a block code, the codeword is 8 bits long. How long is the dataword if the number of valid codewords in this block are 64? How many codewords exist in total?
need problem 6.13 done. 12. The analog signal xa (t) = cos (100mt) + cos (120πt) led using natural sampling as shown in Fig. 6.18. The sampling rate used is f, -4 width of each pulse is τ = 0.5 ms...
need problem 6.13 done.
12. The analog signal xa (t) = cos (100mt) + cos (120πt) led using natural sampling as shown in Fig. 6.18. The sampling rate used is f, -4 width of each pulse is τ = 0.5 ms. Write an analytical expression for the Fourier transform Xa (w) and sketch it. Find an analytical expression for X, () the Fourier transform of the naturally- sampled signal T, (t). a. c. Sketch the transform X, (w). 613. Repeat...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for sampling. Consider a signal x,(t) = cos(40t) cos(80t). Sketch the 2-sided complex spectrum and [5 pts] determine the minimum sampling rate that can be used to sample the signal without causing aliasing. [5 pts] Repeat Part a for the signal x2 t) cos(4 x 103t) sin(3 x 103Tt) cos(8 x 10Tt). [5 pts] Repeat Part a for the signal x3(t) cos(4 x 103Trt) sin(3...
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5)...
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system shown in the figure below, where the two input signals are given to be xi(t) = sinc(10t) and x2(t) = sinc(6t). ylt) z(t) LTI →2;(+) ht) Xalt) P(+) - E81-nt) a) State the sampling theorem. Be sure to include all conditions for its validity. (5 pts) b) What is the minimum frequency at which y(t) must be sampled such that it could be completely...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
1. DSC-SC Modulation. Consider a message signal m(t) = 3 sinc(10t) this is applied to a...
1. DSC-SC Modulation. Consider a message signal m(t) = 3 sinc(10t) this is applied to a product modulator with a carrier wave c(t) = 2 cos(100nt). (a) (5 points) Find and plot the Fourier transform S(f) of the DSB-SC modulated signal s(t). (b) (5 points) What is the bandwidth of s(t)? (c) (5 points) The signal s(t) is next applied to filter h(t), the output of the filter is named y(t). Now assume that I $2/300, If|< 30, H(f) =...
Digital Communication (ELEC 20004)-Spring-19-cW1 (ASSMNT)-All AK 1. a. A waveform m() -62 sin (3500t+)+36 sin(4500t5 is to be uniformly sampled for digital transmission. i. Determine the sampling...
Digital Communication (ELEC 20004)-Spring-19-cW1 (ASSMNT)-All AK 1. a. A waveform m() -62 sin (3500t+)+36 sin(4500t5 is to be uniformly sampled for digital transmission. i. Determine the sampling frequency that satisfies the Nyquist criteria, and hence (7 Marks) determine the period of the signal ii. If we want to reproduce 55 minutes of this wave form, determine the how many (8 Marks) b. The output of a digital computer is at a rate of 64 kbps. If the roll off factors...
please show steps, focus on part b more
1. (23 points) Sampling and Aliasing. (a) Find the Nyquist sampling rate wn for the given x(t). (Recall that the sampling frequency has to be twice larger than the bandwidth of the signal to recover the signal without loss of information.) i. (5 pts) X(t) = sinc(5000) * cos(7t). ii. (5 pts) r(t) = sin(101) cos(106) iii. (5 pts) (t) = sinc(50000) + cos(56) (b) (8 pts) Let r(t) = sinc(t/h), y(t)...
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the sampled signal if the sampling rate is 25% higher than the Nyquist rate. a.) ft)sinc E 2T 10 b.) h)=sinc 2T For all the following, use ft) given in part a.) c.) glt)= f(l-7) d.) c(t)- f)cos() 1 e.) x(t)= fit)+ _ sinc (t
4. Find the Nyquist rate for the following signals. For each case sketch the magnitude spectrum of the...
19. 1 mark) What is the Nyquist sampling rate for a band-pass signal with a bandwidth of 300kHz if the lowest frequency is 100kHz? 20. 1 mark) In a block code, the codeword is 8 bits long. How long is the dataword if the number of valid codewords in this block are 64? How many codewords exist in total?
need problem 6.13 done.
12. The analog signal xa (t) = cos (100mt) + cos (120πt) led using natural sampling as shown in Fig. 6.18. The sampling rate used is f, -4 width of each pulse is τ = 0.5 ms. Write an analytical expression for the Fourier transform Xa (w) and sketch it. Find an analytical expression for X, () the Fourier transform of the naturally- sampled signal T, (t). a. c. Sketch the transform X, (w). 613. Repeat...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for sampling. Consider a signal x,(t) = cos(40t) cos(80t). Sketch the 2-sided complex spectrum and [5 pts] determine the minimum sampling rate that can be used to sample the signal without causing aliasing. [5 pts] Repeat Part a for the signal x2 t) cos(4 x 103t) sin(3 x 103Tt) cos(8 x 10Tt). [5 pts] Repeat Part a for the signal x3(t) cos(4 x 103Trt) sin(3...
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system shown in the figure below, where the two input signals are given to be xi(t) = sinc(10t) and x2(t) = sinc(6t). ylt) z(t) LTI →2;(+) ht) Xalt) P(+) - E81-nt) a) State the sampling theorem. Be sure to include all conditions for its validity. (5 pts) b) What is the minimum frequency at which y(t) must be sampled such that it could be completely...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
1. DSC-SC Modulation. Consider a message signal m(t) = 3 sinc(10t) this is applied to a product modulator with a carrier wave c(t) = 2 cos(100nt). (a) (5 points) Find and plot the Fourier transform S(f) of the DSB-SC modulated signal s(t). (b) (5 points) What is the bandwidth of s(t)? (c) (5 points) The signal s(t) is next applied to filter h(t), the output of the filter is named y(t). Now assume that I $2/300, If|< 30, H(f) =...
Digital Communication (ELEC 20004)-Spring-19-cW1 (ASSMNT)-All AK 1. a. A waveform m() -62 sin (3500t+)+36 sin(4500t5 is to be uniformly sampled for digital transmission. i. Determine the sampling frequency that satisfies the Nyquist criteria, and hence (7 Marks) determine the period of the signal ii. If we want to reproduce 55 minutes of this wave form, determine the how many (8 Marks) b. The output of a digital computer is at a rate of 64 kbps. If the roll off factors...
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