Description

Problem 1: Using filter and difference equation

Matlab provides the filter function which is a Direct Form-II transposed implementation of the standard difference equation. Such functions save coding time and help us to focus more on the system behavior.

1. Re-do problem-3 of Classwork-2 and implement using the ‘filter’ command to filter out the high frequency components of the ECG signal.
2. Instead of using ‘filter’ command, convolute the ECG signal with h = [1/3, 1/3, 1/3] using ‘conv’ Compare the result with that of (a).
3. Write your own convolution function and re-do (b) using your convolution function.

Problem 2: Basics about sinusoids and sampling rate

Let the sampling rate fs be 50 Hz, and the time array t varies from 0 to 1 second.

1. Create and plot a sine signal 𝒚_𝟏(𝒕) = 𝐬𝐢𝐧(𝟐𝝅𝒇_𝟏𝒕), where 𝒇_𝟏 = 𝟏𝟎 𝑯𝒛
2. Create and plot a sine signal 𝒚_𝟐(𝒕) = 𝐬𝐢𝐧(𝟐𝝅𝒇_𝟐𝒕), where 𝒇_𝟐 = 𝟔𝟎 𝑯𝒛
3. Can you differentiate between 𝒚_𝟏(𝒕) and 𝒚_𝟐(𝒕) plot? Why?

Problem 3: Signal data to sound

Let the sampling rate fs be 50 kHz, and the time t varies from 0 to 1 second.

1. Create and plot a 2 kHz signal 𝒚_𝟏(𝒕) = 𝐬𝐢𝐧(𝟐𝝅𝒇_𝟏𝒕) using Matlab. Let the horizontal axis vary from 0 to 0.01 second. Use the command ‘sound(signal, sampling rate)’ to listen the tone.
2. Create, plot and listen to the sine signal 𝒚_𝟐(𝒕) = 𝐬𝐢𝐧(𝟐𝝅𝒇_𝟐𝒕), where 𝒇_𝟐 = 𝟔 𝒌𝑯𝒛. How different is the sound of y₂ in comparison to the sound of y₁?
3. Create, plot and listen to the sine signal 𝒚_𝟑(𝒕) = 𝐬𝐢𝐧(𝟐𝝅𝒇_𝟑𝒕), where 𝒇_𝟑 = 𝟐𝟓 𝒌𝑯𝒛. Can you still hear the sound?