MATLAB Numerical Assignment

Exercise 1: Find a short MATLAB expression to build the matrix.

Exercise 2: Give a MATLAB expression that uses only a single matrix multiplication with B to obtain

(a) the sum of columns 5 and 7 of B

(b) the last row of B

(c) a version of B with rows 2 and 3 swapped

Exercise 3: Give a MATLAB expression that multiplies two vectors to obtain.

Exercise 4: Modify slide 30 to produce tones of falling frequency instead.

Exercise 5:

(a) Write down the function g(t) that has the shape of a sine wave that increases linearly in frequency from 0 Hz at t = 0 s to 5 Hz at t = 10 s.

(b) Plot the graph of this function using MATLAB’s plot command.

(c) Add to the same figure (this can be achieved using the hold command) in a different colour a graph of the same function sampled at 5 Hz, using the stem command.

(d) [Extra credit] Plot the graph from (c) separately. Can you explain its symmetry?

Exercise 6: Use MATLAB to write an audio waveform (8 kHz sampling frequency) that contains a sequence of nine tones with frequencies 659, 622, 659, 622, 659, 494, 587, 523, and 440 Hz. Then add to this waveform a copy of itself in which every other sample has been multiplied by ?1. Play the waveform, write it to a WAV file, and use the specgram command to plot its spectrogram with correctly labelled time and frequency axis.

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