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April 7th, 2014, 09:52 AM   #1
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FIR frequency response

I finally thought it would be a good idea to take a look at FIR filters and have started looking at the math for it.
I can generate coefficients for the filter, they match an example I found on the web:
FIR Filters by Windowing - The Lab Book Pages

My problem is, how do I view the frequency response? None of the math I've tried gives me a graph that looks like the example. I seem to have lost the math I used, it basically ran a bunch of cosines through the tap array, something like freq[m] = sum-of [cos (2 * Pi * h(n) * m)] for n= 0 to 20
repeating for m=0 to 20
Where h(n) is the FIR tap array

Any idea what I'm supposed to do?
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April 8th, 2014, 01:55 AM   #2
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I think I finally have it!

given that the example only uses 21 taps, having a frequency plot with only 21 points simply doesn't show enough information, So I multiplied the number of output samples in the frequency by a 'factor'.

In case anyone is interested, here's my Excel VBA code to solve it:

factor = 10

For j = 0 To (M / 2) * factor
Rtot = 0
Itot = 0
For n = 0 To M
Am = Worksheets("Sheet1").Cells(n + 1, 1)
Re = Am * Cos(2 * Pi * j * n / Taps / factor)
Im = -Am * Sin(2 * Pi * j * n / Taps / factor)
Rtot = Rtot + Re
Itot = Itot + Im
tot = ((Rtot ^ 2) + (Itot ^ 2)) ^ 0.5
Worksheets("Sheet1").Cells(j + 1, 3) = 20 * Log(tot)

Taps is 21 and M is Taps-1 (as per the example). the tap values are in "Sheet1" column A, output is "Sheet1" column C
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April 9th, 2014, 12:50 AM   #3
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Hmmm, although it gives me the right general shape, the amplitudes are off. It looks fine up until the cutoff frequency, it's a little too steep, the first 'hump' is at -50dB instead of about -20dB as per the graph in the example.
I believe I've found a small error, in my Cos and Sin maths, Taps should be M, giving:
Re = Am * Cos(2 * Pi * j * n / M / factor)
Im = Am * Sin(2 * Pi * j * n / M / factor)
The amplitude graph (an array of 'tot') looks the same as the example, but my dB graph doesn't [ 20*Log(tot) ]

Anyone ideas?
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April 15th, 2014, 06:49 PM   #4
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Math Focus: Electrical Engineering Applications
Hi weirddave,

I think that Log() in VBA is the natural log. When I used the natural log instead of the common log in my simulation, the first hump was also around -50 dB. If you divide by Log(10) does it look right?

Also, in your equation for the imaginary term, the minus sign disappeared. For the magnitude this does not matter, but it reverses the phase.
Thanks from weirddave
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April 16th, 2014, 12:04 AM   #5
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It does look like the minus sign disappeared, what I didn't mention was that when I changed those equations, I also moved the minus:
Itot = Itot - Im

Just divided by log(10), brilliant That's done the trick! Woohoo!
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