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This module describes how to implement an FIR filter using a FIFO buffer where the elements are shifted and another that uses a circular buffer.

Introduction

This module explains how to implement an FIR filter in the Direct-Form structure. It explains how data is stored as samples are received and how to use a circular buffer in the algorithm.

Reading

Fir filtering

The difference equation for an N -order FIR filter is given by:

y ( n ) = k = 0 N 1 b k x ( n k ) = k = 0 N 1 h ( k ) x ( n k ) size 12{y \( n \) = Sum cSub { size 8{k=0} } cSup { size 8{N - 1} } {b rSub { size 8{k} } x \( n - k \) } = Sum cSub { size 8{k=0} } cSup { size 8{N - 1} } {h \( k \) x \( n - k \) } } {}

For each new input sample, x ( n ), the filter produces an output y ( n ). To calculate the new output sample, the input must be convolved with the FIR filter impulse response, h ( n ). Notice that the summation requires the input samples starting with the most recent sample, x ( n ) through the N -1 most recent samples, through x ( n - N -1). In a DSP system, these previous samples must be saved in an array in memory. Usually there will be one new sample received, x ( n ), and any previous samples that were received must be saved in memory.

Fifo buffer

Since the algorithm only needs the previous N -1 samples to be saved there must be a way for the algorithm to update the array when a new sample is input. This can be accomplished in two ways. The first way is to shift all the samples in the array by copying them to the shifted location and then storing the new value at the beginning of the array. This is a first-in-first-out (FIFO) buffer. If this method is used then the FIR algorithm is given by

y out = k = 0 N 1 h ( k ) x saved ( k ) size 12{y rSub { size 8{ ital "out"} } = Sum cSub { size 8{k=0} } cSup { size 8{N - 1} } {h \( k \) x rSub { size 8{ ital "saved"} } \( k \) } } {}

Figure 1 shows a diagram of the implementation of the FIR filter using the array shifting method. In the diagram the "*" indicates multiplication. The new value is shifted into the x (0) spot and all the others are shifted to the right.

Diagram of the FIR filter implementation using the shifting method

The following pseudo-code shows how to implement the FIR filter using the FIFO type buffer. In the code the following definitions are used:

N - number of coefficients

h(n) - filter coefficients, n = 0...N-1

x(n) - stored input data, n = 0...N-1

input_sample - variable that contains the newest input sample

// Shift in the new sample. Note the data is shifted starting at the end. for (i=N-2; i>=0; i--){ x[i+1]= x[i];} x[0]= input_sample // Filter the dataynew = 0; for(i=0;i<N;i++){ ynew = ynew + h(i)*x(i);}

Double size fifo buffer

In the example above, the data in the FIFO buffer is shifted every time a new sample is received. This could lead to inefficient code. It is better to do processing on blocks of data. For instance, you could use a DMA to copy a block of data from one place to another and free up the processor from doing the work.

One solution could be to make a FIFO buffer that is twice as large as the data that is needed to store. When this is done, shifting of the data can be done after a block of data is received.

The following figures show the data buffer as data is being received and stored. Figure 2 shows the buffer when the first new value is received. Of course the buffer would be zeroed before processing begins. The shaded area shows the part of the buffer that is used in the algorithm.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
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Brian Reply
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
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What is meant by 'nano scale'?
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Santosh
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what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Dsp lab with ti c6x dsp and c6713 dsk. OpenStax CNX. Feb 18, 2013 Download for free at http://cnx.org/content/col11264/1.6
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