4.
For a
signal x(n)=sin(2*pi*n/3) defined for n=0to7, evaluate the Fast
Fourier Transform using signal flow graph. (Use decimation in
frequency Algorithm)
What increase in speed can be expected in using a fast Fourier
transform algorithm rather than direct arithmetic to compute the
Fourier transform of an image of size 1024 × 1024?
Fourier Transform. Discuss the effects of multiplying a time
domain signal by a sinusoid (including multiple times) has on both
the time and frequency domain representations, as well as the
practical use of the method, i.e. summarize the conceptual
understanding within 100 words.
Given a sinusoidal signal:
x(t) = Asin(2πft)
Find Fourier Transform (FT) of the sinusoidal x(t) given above
and plot the spectrum with:
a. A = 2, f = 1000Hz
b. A = 2, f = 9000Hz
c. A = 5, f = 1000Hz
d. A = 10, f = 10000Hz
Both the Fourier Series and the Discrete Fourier Transform are
calculated using summation. Explain the key differences in what the
inputs each of the Fourier Series and the DFT are AND the
requirements the inputs.