Lab 4: theory

Introduction

In this lab you are going to apply the Fast Fourier Transform ( FFT ) to analyze the spectral content of an input signal in real time. After computing theFFT of a 1024-sample block of input data, you will then compute the squared magnitude of the sampled spectrum and sendit to the output for display on the oscilloscope. In contrast to the systems you have implemented in the previous labs, theFFT is an algorithm that operates on blocks of samples at a time. In order to operate on blocks of samples, you will needto use interrupts to halt processing so that samples can be transferred.

A second objective of this lab exercise is to introduce the TI-C549 C environment in a practical DSP application. In future labs,the benefits of using the C environment will become clear as larger systems are developed. The C environment provides a fast andconvenient way to implement a DSP system using C and assembly modules.

The FFT can be used to analyze the spectral content of a signal. Recall that the FFT is an efficient algorithm forcomputing the Discrete Fourier Transform ( DFT ), a frequency-sampled version of the DTFT .

DFT:

Your implementation will include windowing of the input data prior to the FFT computation. This is simple a point-by-pointmultiplication of the input with an analysis window. As you will explore in the prelab exercises, the choice of windowaffects the shape of the resulting window.

A block diagram representation of the spectrum analyzer you will implement in the lab, including the required input andouput locations, can be found depicted in .