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Introduction to MATLAB
– exercises and solution notes
Markus Kuhn
Michaelmas 2015 – Part II
Exercise 1: Find a short MATLAB expression to build the matrix
B =
Answer: b = [1:7; 9:-2:-3; 2.^(2:8)]
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
Answer: b * [0 0 0 0 1 0 1]'
(b) the last row of B
Answer: [0 0 1] * b
(c) a version of B with rows 2 and 3 swapped
Answer: [1 0 0; 0 0 1; 0 1 0] * b
Exercise 3: Give a MATLAB expression that multiplies two vectors to obtain
(a) the matrix
Answer: [1 1 1]' * (1:5)
(b) the matrix
Answer: (0:4)' * [1 1 1]
Exercise 4: Modify slide 30 to produce tones of falling frequency instead.
Answer: Replace
f = fmin * (fmax/fmin) .^ l;
with
f = fmax * (fmin/fmax) .^ l;
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.
Answer: The instantaneous frequency of function g(t) at time t is
f (t) = t · 5 Hz 10 s = t 2 s^2 and since the phase of a sine wave is 2π times the integrated frequency so far, we get
g(t) = sin
( 2 π
∫ (^) t
0
f (t′) dt′
) = sin
( 2 π t
2 4 s^2
) = sin
( πt^2 2 s^2
)
(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.
Answer: for (b) and (c)
f = [659 622 659 622 659 494 587 523 440]; fs = 8000; % sampling frequency d = 0.5; % duration per tone t = 0:1/fs:d-1/fs; w = sin(2 * pi * f' * t)/2; w = w'; w = w(:)'; w = [w, w .* (mod((1:length(w)), 2) * 2 - 1)]; audiowrite('matlab_answer-2.wav', w, fs); specgram(w, [], fs);
Time
1 2 3 4 5 6 7 8
Frequency
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