Experiment 4 : Fourier Transform


Fourier Transform converts a signal from time domain to frequency domain. Fourier transform is extensively used in signal processing. In this experiment, we performed Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT).
DFT
In DFT discrete time signal is converted to discrete frequency representation.  The signal converted to frequency domain can be converted back to time domain using Inverse Discrete Fourier Transform (IDFT). However, DFT is a slow process and works well when the signal length is not too large.
FFT
Again, in FFT, the signal is converted to frequency domain, however, this method outranks DFT. This is simply because in this method the input signal is decomposed into smaller signals thus enabling faster computation. Also in this method parallel computation takes place thus making it a faster process. 

Comments

  1. Unknown24 April 2019 at 03:06

    Fourier transformation was discovered just as a logical pattern/waveform. Its wonderful to see that it's being used very effectively in core fields

    ReplyDelete
  2. Anonymous24 April 2019 at 05:07

    Never knew Fourier series and transformation was so useful in studying signals

    ReplyDelete
  3. Luke Shawn Thomas24 April 2019 at 23:32

    Really wished this article was a little simplified; not all of us are Newton's or Einsteins

    ReplyDelete

Post a Comment

Popular posts from this blog

Experiment 5 : Linear Filtering using OAM/OSM

In this experiment, we learnt about linear FIR filtering methods i.e. OAM and OSM. These are two algorithms that are used to process real-time signals. This is used over Fast Fourier Transform (FFT) because in case of FFT, the entire signal needs to be available at the same time in order to receive the output which isn’t feasible in real-time signals. Here’s where OAM and OSM come into play. In the lab, we implemented the required codes on the DSP board and saw how real-time signals are processed. Overlap-Add Method (OAM) Here the input sequence is x(n) and an M point sequence h(n) is considered. The long input signal x(n) is further decomposed into L point sequences. With the formula N = L + M -1, where N is assumed to be a radix 2 value, we get the value of L. After decomposing we perform Linear convolution of each decomposed signal and add all of them to get the final output signal. Overlap Save Method (OSM) In this method, again we decompose the signal in the same way ...
Read more

Experiment 1: Simulator

In this experiment, we simulated various techniques on CCS version 4. To get a hang of simulation, we first simulated a normal sine wave. Next, we simulated a Harmonic wave of frequency 60 Hz. We then simulated the various modulation techniques i.e. BPSK, QPSK and DPSK. Also, we simulated a few line coding techniques i.e. Manchester Coding, Duo-Binary Coding, Modified Duo- Binary coding and Duo-binary coding with precoder. This experiment was very helpful as it helped it us visualize and understand things better.
Read more