1. Given three sinusoids with the following amplitude and phases: x 1 (t) = 5 cos (2 (500)t) x 2 (t) = 5 cos (2

1. Given three sinusoids with the following amplitude and phases:

x ₁ (t) = 5 cos (2π (500)t)

x ₂ (t) = 5 cos (2π (1200)t + 0.25π )

x ₃ (t) = 5 cos (2(1800)t + 0.5π )

a. Create a MATLAB program to sample each sinusoid and generate a sum of three sinusoids, that is, x(n) = x ₁ (n) + x ₂ (n) + x ₃ (n), using a sampling rate of 800 Hz, and plot the sum x(n) over a range of time that will exhibit approximately 0.1 second.

2. b. Use the MATLAB function fft() to compute DFT coefficients, and plot and examine the spectrum of the signal x(n).

a. Generate the sum of sinusoids for 240 samples using a sampling rate of 8000 Hz.

b. Write a MATLAB program to compute and plot the amplitude spectrum of the signal x(n) with the FFT and using each of the following window functions:

(1) Rectangular window (no window)

(2) Triangular window

(3) Hamming window

c. Examine the effect of spectral leakage for each window used in (b).