Digital Signal Processing with

LabVIEW 8.6

Lab # 08

Spectral Analysis using FFT (Fast Fourier

Transform)

Adnan Niazi

Lab Engineer

Signal Processing/Signal & Systems Lab

CECOS University of IT & Emerging Sciences

10th- 11th April 2009

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Agenda

▌ What is Fourier Transform

▌ What is Discrete Fourier Transform

▌ What is Fast Fourier Transform

▌ Characteristics of FFT

▌ Windowing

▌ Why use Windowing

▌ Effect of Windowing on FFT

▌ Types of Windows

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Fourier Transform

▌ Fourier transform is used to view the spectral contents

of an analog signal

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CECOS University of IT & Emerging Sciences

Discrete Fourier Transform

▌ Fourier transform can only be used for analog signals

▌ Discrete Fourier Transform is used for to find the

spectral composition of digital signals

 where x is the input sequence, X is the DFT, and n is the

number of samples in both the discrete-time and the

discrete-frequency domain

 n is also reoffered to as the window size

 To calculate the discrete Fourier transform the DSP will

need to perform n2 complex operations

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Fast Fourier Transform (FFT)

▌ Fast Fourier Transform performs the same function as

discrete Fourier transform

▌ However, FFT requires only nlog2(n) operations.

▌ Thus FFT is a much more computationally efficient

algorithm compared to DFT

Contact: [email protected]

CECOS University of IT & Emerging Sciences

FFT

▌ To calculate FFT two parameter are very important

 sampling rate fs

 block size N

▌ If Block size N is 512 it means that FFT is calculated

from 512 time domain samples. The FFT will generated

512 frequency domain samples.

▌ The 0th sample will represent 0Hz and the 511th sample

will represent fs

▌ Thus the multiplication factor for the FFT should be

fs/(N-1)

Contact: [email protected]

CECOS University of IT & Emerging Sciences

FFT

▌ If a signal is sampled at fs Hz than it means that the

highest frequency that it contains is fs/2 Hz

▌ This implies that FFT is only significant from 0 Hz - fs/2

Hz or (0 to (N/2)-1) samples

▌ The second relationship links the frequency resolution

(f) to the total acquisition time (T), which is related to the

sampling frequency (fs) and the block size(N) of the FFT

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CECOS University of IT & Emerging Sciences

FFT (Front Panel)

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FFT (Block Diagram)

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The Higher the N, finer the FFT

▌ FFT of a 10KHz signal sampled at 48Khz using a 128

point FFT

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CECOS University of IT & Emerging Sciences

The Higher the N, finer the FFT

▌ FFT of a 10KHz signal sampled at 48Khz using a 512

point FFT

Contact: [email protected]

CECOS University of IT & Emerging Sciences

The Higher the N, finer the FFT

▌ FFT of a 10KHz signal sampled at 48Khz using a 1024

point FFT

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Windowing

▌ For FFT to be accurate the input signal must infinite

▌ In actual practice the DSP can only process a certain

number of samples(N) at a time. It can’t process infinite

samples all at once.

▌ Discontinuities are seen by the DSP processors which

results in spectral widening

▌ This is known as Spectral Leakage

▌ The cure for this problem is Windowing

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Why Use Windowing

NN samples being

Next N samples

Acquired by DSP

being Acquired by

FFT being

for calculating

Calculated

DSP for

FFT

calculating FFT

A huge discontinuity

is seen by the DS

processor in the

incoming data

although original has

no discontinuity. This

result sin Spectral

Leakage

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CECOS University of IT & Emerging Sciences

Windowing

▌ Windowing lessens the spectral leakage by taking the

signal to zero at the end.

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CECOS University of IT & Emerging Sciences

Signal after Windowing

NN samples being

Next N samples

Acquired by DSP

being Acquired by

FFT being

for calculating

Calculated

DSP for

FFT

calculating FFT

Contact: [email protected]

CECOS University of IT & Emerging Sciences

FFT with and without Windowing

FFT without Windowing

FFT with Windowing

Spectral

Leakage is

Leakage

Reduced

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Types of Windows

▌ Hanning Widow

▌ Hamming Window

▌ Blackman Window

▌ Blackman - Harris Window

▌ Blackman - Nuttall

▌ Exact Blackman Window

▌ Cosine Window

▌ Cosine Tapered Window

▌ Kaiser Window

▌ Gaussian Window

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CECOS University of IT & Emerging Sciences

Types of Windows

▌ Bohman Window

▌ Rectangular Window

▌ Exponential Window

▌ Chebychev Window

▌ Dolph - Chebychev Window

▌ Parzen Window

▌ Flat Top Window

▌ Welch Window

▌ Bartlett Hanning Window

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Filtering

▌ Filtering removes unwanted signals from the wanted

ones

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CECOS University of IT & Emerging Sciences

Types of Filtering

▌ Analog Filtering

▌ Digital Filtering

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Analog Filtering

▌ Analog filters work on signals in continuous time

domain

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CECOS University of IT & Emerging Sciences

Types of Analog Filters

▌ Analog filters are of three types:

 Passive Filters

• Made from Resistors, Capacitors and Inductors

 Active Filters

• Made from Opamps, Resistors and Capacitors

 Switched Capacitor Filters

• Made from Switched capacitors

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Analog Filter Topologies

▌ Butterworth Filter

▌ Bessel Filter

▌ Besselworth Filter

▌ Chebychev Filter

▌ Inverse Chebychev Filter

▌ Elliptic and Cauer Filter

▌ Gaussian 6dB Filter

▌ Gaussian 12dB Filter

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Why Digital filters better than Analog Filtering

▌ Analog filters become unstable when the order is

increased beyond 10

▌ This means that you can’t make filters with very steep

roll offs

▌ Digital filters are more accurate where as analog filters

are susceptible to variation in their response due to drift

and tolerance in component values

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Digital Filter

▌ Digital filters work on

samples in discrete time

domain

▌ Digital filtering can be

carried out on a

 DSP

 FPGA

 & to some extent on a

microcontroller

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Task 1

▌ Design a Stereo VU Meter

 Each channel must be assigned four LEDs on the DSP kit

 The front panel must have Digital and Analog VU Meter

for both audio channels

 The audio output to the headphones must be stereo as

well

 The Digital VU meter on the Front Panel must be lying

horizontal

 Attenuation of the incoming Audio Signals must be

controlled from a single slider

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Task 1: Stereo VU Meter

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CECOS University of IT & Emerging Sciences

Task 2

▌ Play the Spartan3E-launch.wmv Video and observe the

stereo VU meter and decide whether the audio is mono

or Stereo.

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Task 3

▌ Play the Brain operated Keyboard from gTEC

Austria.wmv and observe the stereo VU meter and

decide whether the audio is mono or Stereo.

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Task 4

▌ Play the zelprint.wmv and observe the stereo VU meter

and decide whether the audio is mono or Stereo.

Contact: [email protected]

CECOS University of IT & Emerging Sciences

Lab Report 5

▌ The lab Report must contain

 A picture of the front panel

 A picture of the block diagram

 A precise one line answer to Task 2

 A precise one line answer to Task 3

 A precise one line answer to Task 4

 Always Write Full Question before beginning to answer it

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CECOS University of IT & Emerging Sciences

Electronic Paint Brush

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CECOS University of IT & Emerging Sciences