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Home/digital signal processing

electricalstudent Latest Articles

On: October 31, 2023 Posted in digital signal processing Comments: 0

P2.4Let x(n) = {2,4, -3, 1, -5, 4, 7}. Generate and plot the samples (use the stem function) of the following sequences.

P2.4
Let x(n) = {2,4, -3, 1, -5, 4, 7}. Generate and plot the samples (use the stem function) of
the following sequences.

  1. x1(n) = 2x(n – 3) + 3x(n + 4) – x(n)
  2. x2 (n) = 4x(4 + n) + 5x(n + 5) + 2x(n)
  3. x3 (n) = x(n + 3)x(n – 2) + x(1 – n)x(n + 1)
  4. x4 (n) = 2e0.5𝑛x(n) + cos(0.1πn) x(n + 2) , -10 ≤ n ≤ 10

sigshift.m is required for this which is attached here

unction [y,n] = sigshift(x,m,n0)

% implements y(n) = x(n-n0)

% -------------------------

% [y,n] = sigshift(x,m,n0)

%

n = m+n0; y = x;
(more…)
On: October 31, 2023 Posted in digital signal processing Comments: 0

Generate the following random sequences and obtain their histogram using the hist function with 100 bins. Use the bar function to plot each histogram.

Generate the following random sequences and obtain their histogram using the hist function with 100 bins. Use the bar function to plot each histogram.

  1. x1(n) is a random sequence whose samples are independent and uniformly distributed over [0, 2] interval. Generate 100,000 samples.
  2. x2(n) is a Gaussian random sequence whose samples are independent with mean 10 and variance 10. Generate 10,000 samples.
  3. x3(n) = x1(n) + x1(n – 1) where x1(n) is the random sequence given in part 1 above. Comment on the shape of this histogram and explain the shape.
  4. x4(n) = Σy𝑘(n)4𝑘=1 where each random sequence y𝑘(n) is independent of others with samples uniformly distributed over [-0.5, 0.5]. Comment on the shape of this histogram.
(more…)
On: October 31, 2023 Posted in digital signal processing Comments: 0

Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations discussed in this chapter. Plot signal samples using the stem function.

  1. x1(n) = 3δ(n + 2) + 2δ(n) – δ(n – 3) + 5δ(n – 7), -5 ≤ n ≤ 15.
  2. x2(n) Σe−|k|5k=−5=δ(n – 2k), -10 ≤ n ≤ 10.
  3. x3(n) = 10u(n) – 5u(n – 5) – 10u(n – 10) + 5u(n – 15).
  4. x4(n) = e0.1n[u(n + 20) – u(n – 10)].
  5. x5(n) = 5[cos(0.49πn) + cos(0.51πn)], -200 ≤ n ≤ 200. Comment on the waveform shape.
  6. x6(n) = 2 sin(0.01πn)cos(0.5πn), -200 ≤ n ≤ 200. Comment on the waveform shape.
  7. x7(n) = e−0.05n sin(0.1πn + π/3), 0 ≤ n ≤ 100. Comment on the waveform shape.
  8. x8(n) = e0.01n sin(0.1πn), 0 ≤ n ≤ 100. Comment on the waveform shape.
Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations discussed in this chapter. Plot signal samples using the stem function.
Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations discussed in this chapter. Plot signal samples using the stem function.
to solve this problem we need impseq.m function which is provided here 
function [x,n] = impseq(n0,n1,n2)
% Generates x(n) = delta(n-n0); n1 <= n,n0 <= n2
% ----------------------------------------------
% [x,n] = impseq(n0,n1,n2)
%
if ((n0 < n1) | (n0 > n2) | (n1 > n2))
	error('arguments must satisfy n1 <= n0 <= n2')
end
n = [n1:n2];
%x = [zeros(1,(n0-n1)), 1, zeros(1,(n2-n0))];
x = [(n-n0) == 0];
Read more: Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations discussed in this chapter. Plot signal samples using the stem function. (more…)