Lab 1: Introduction to Python3 Solution

Description

1. Write a Python3 function mysinplotthat takes in 3 arguments: frequency fin Hz, sampling frequency fsin Hz, and number of cycles _{n T1,}and plots exactly nperiods of a sine func ion of frequency f Hz, sampled at f_s Hz. In the report, briefly describe your logic, and give a few example plo s.

2. Let x(t) = sin(2p f t), t 2 [ T, T], T > 0 and zero elsewhere. Consider the signal y(t) = x( ), t 2 [ T₁, T₁], T₁ > 0 and zero elsewhere. In order to simulate and com-pute the amplitude spectrum of x, we will sample the signal y at f_s Hz in order to obtain a sampled sequence denoted by y_d, and apply Discrete Fourier transform on y_d (using fft). Write a function myctftthat takes in T, fs, and plots the amplitude

spectrum of y. The x-axis must be scaled appropriately to show frequency in Hz.

1. Show a few example plots with different values for the input parameters.

2. Given f = 10Hz, T = 1sec, analytically compute the Fourier transform of x, and using appropriate values of T₁ and f_s try to obtain the amplitude spectrum as close as possible to the analytical result using your code, with proper justification.

3. What happens when we set T = T₁, and why?

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