This repository contains various signals analysis projects I did in 2020 and 2021. I have also added the finall project in this repository. For these, I followed the book Signals and Systems, Book by Alan V. Oppenheim
and 
This project generates echo in sound waves using matlab.
You can add your own audio in to the program or also record your own audio. I have also added a feature where you can control the reverb and output amplitude ( just like a DJ's sound controller ) in the code :
This is the function for the project. This will have 4 parameters
- 1st is the input signal
- 2nd is the sampling frequency
- 3rd is the reverb delay length in seconds
- 4th is the amplitude of echo sound
- Development of an 7th order Butterworth filter and plotting the B(s)B(-s) signal
For my case, the filter is a low pass normalizing filter and hence, the poles would lie on the boundary of the circle r = Wc.
| B(s) | B(s)B(-s) |
|---|---|
 |
 |
The transfer function obtained is as follows :
- Plotting the FFT of a combination of 2 simple sinusoidal signals and developing its magnitude spectrum
In the magnitude specturm, I observed the following points:
- All the 4 peaks have a magnitude nearing to 2 i.e. the magnitude or amplitude of the original cosine functions.
- The graph has 4 peaks and I will justify them one by one:
- 1st peak – It is at frequency of 507Hz owing to sig_1 or the cosine corresponding to 507Hz frequency in input signal.
- 2nd peak – It is basically formed to represent (-11507) Hz frequency. {2cos x = e^jx + e^-jx}. So, it’s the -jx part and because of change in axis, the frequency is shown over here.
- 3rd peak – It shows 11507 Hz frequency. Now because of constraints in axis and due to time period complications in FFT, it is shown as (20000 – 11507 ) Hz .
- 4th peak - It is owing to the -507 Hz frequency and is formed in symmetry, just like peak 2 is formed.
- Generating complex convolutions in continuous time domain
- Generating complex convolutions in discrete time domain
- Given a system defination, developing a pole-zero map to comment on its stability.
Given the signal 
,
the pole-zero map is as follows:
The stability analysis is as follows:
- For the system to be stable and causal, mode(z) must be greater than the mode(poles).i.e. the system must be completely right-handed or on the positive axis of time. Which is proved by the hand calculations above.
- Also, the poles marked on the left side of the real axis, this means that the system is bounded . It has no exponentially increasing component
- Generation of a hybrid signal and applying time-scaling and time-shifting to that.
- Generation of a standard signal and applying time-scaling and time-shifting to that.
