# Connexions

You are here: Home » Content » Spectrum Analyzer: MATLAB Exercise

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• TI DSP

This module is included inLens: Texas Instruments DSP Lens
By: Texas InstrumentsAs a part of collection: "DSP Laboratory with TI TMS320C54x"

Click the "TI DSP" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

#### Also in these lenses

• Lens for Engineering

This module is included inLens: Lens for Engineering
By: Sidney Burrus

Click the "Lens for Engineering" link to see all content selected in this lens.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

# Spectrum Analyzer: MATLAB Exercise

Summary: You will investigate the effects of windowing and zero-padding on the Discrete Fourier Transform of a signal.

## MATLAB Exercise

Since the DFT is a sampled version of the spectrum of a digital signal, it has certain sampling effects. To explore these sampling effects more thoroughly, we consider the effect of multiplying the time signal by different window functions and the effect of using zero-padding to increase the length (and thus the number of sample points) of the DFT. Using the following MATLAB script as an example, plot the squared-magnitude response of the following test cases over the digital frequencies ω c = π8 3π8 ω c 8 3 8 .

1. rectangular window with no zero-padding
2. hamming window with no zero-padding
3. rectangular window with zero-padding by factor of four (i.e., 1024-point FFT)
4. hamming window window with zero-padding by factor of four

Window sequences can be generated in MATLAB by using the boxcar and hamming functions.



1  N = 256;                % length of test signals
2  num_freqs = 100;        % number of frequencies to test
3
4  % Generate vector of frequencies to test
5
6  omega = pi/8 + [0:num_freqs-1]'/num_freqs*pi/4;
7
8  S = zeros(N,num_freqs);                 % matrix to hold FFT results
9
10
11  for i=1:length(omega)                   % loop through freq. vector
12     s = sin(omega(i)*[0:N-1]');          % generate test sine wave
13     win = boxcar(N);                     % use rectangular window
14     s = s.*win;                          % multiply input by window
15     S(:,i) = (abs(fft(s))).^2;           % generate magnitude of FFT
16                                          % and store as a column of S
17  end
18
19  clf;
20  plot(S);                                % plot all spectra on same graph
21



Make sure you understand what every line in the script does. What signals are plotted?

You should be able to describe the tradeoff between mainlobe width and sidelobe behavior for the various window functions. Does zero-padding increase frequency resolution? Are we getting something for free? What is the relationship between the DFT, Xk X k , and the DTFT, Xω X ω , of a sequence xn x n ?

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks