Signal Processing Flashcards

Which MATLAB function computes the Fast Fourier Transform of a signal vector x?

Answer: fft(x)

The `fft(x)` function computes the discrete Fast Fourier Transform of the input vector x in MATLAB.

What inputs does the MATLAB `filter(b, a, x)` function require?

Answer: Numerator coefficients b, denominator coefficients a, and input signal x

`filter(b, a, x)` applies a digital filter defined by numerator coefficients b and denominator coefficients a to the signal x.

According to the Nyquist-Shannon theorem, what is the minimum sampling rate required to reconstruct a signal with maximum frequency f_max?

Answer: 2 * f_max

The Nyquist theorem states the sampling rate must be at least twice the highest frequency component (2 * f_max) to avoid aliasing.

Which MATLAB function designs a FIR filter using the window method given filter order n and normalized cutoff frequency Wn?

Answer: fir1(n, Wn)

`fir1(n, Wn)` designs a windowed linear-phase FIR filter of order n with normalized cutoff frequency Wn.

What does the MATLAB `freqz(b, a)` function compute?

Answer: The frequency response of a digital filter defined by coefficients b and a

`freqz(b, a)` computes and plots the magnitude and phase frequency response of the digital filter with coefficients b and a.

Which MATLAB function computes the linear convolution of two discrete-time sequences u and v?

Answer: conv(u, v)

`conv(u, v)` returns the convolution of vectors u and v, producing an output of length length(u)+length(v)-1.

In MATLAB, how do you generate a 1 Hz sine wave sampled at 100 Hz for 1 second?

Answer: x = sin(2*pi*1*t); where t = 0:1/100:1

A 1 Hz sine wave requires `sin(2*pi*f*t)` with f=1 and a time vector t sampled at 100 Hz (step = 1/100).