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Thread Subject:
Normalized frequency conversions

Subject: Normalized frequency conversions

From: Maya

Date: 5 Jul, 2010 19:14:04

Message: 1 of 2

Matlab explicitly states that:
"All of the non-object oriented filter design functions operate with normalized frequencies. Convert frequency specifications in Hz to normalized frequency to use these functions. The Signal Processing Toolbox software defines normalized frequency to be in the closed interval [0,1] with 1 denoting π radians/sample. For example, to specify a normalized frequency of π/2 radians/sample, enter 0.5.
To convert from Hz to normalized frequency, multiply the frequency in Hz by two and divide by the sampling frequency." --> f(norm) = f(Hz)*2/F(sampl)
What I would like to ask is:
Does that mean that, for example, in a Magnitude (dB) diagram in fvtool using freqz function, the normalized frequency in point labeled 1 on the horizontal axis (that is, =pi since 1 corresponds to pi as stated underneath the axis) corresponds to Herz frequency in this way: f(Hz) = F(sampl)*f(norm)/2 = 8192*pi/2 = 4096*pi Herz??
(where F(sampl) = 8192 by default when ploting with the freqz function)

Subject: Normalized frequency conversions

From: Rick Rosson

Date: 5 Jul, 2010 20:32:25

Message: 2 of 2



Frequncy in different units of measure


 Normalized Angular Regular Angular
                    (discrete) (continuous)

  alpha phi f omega

                     Radians Radians
 pi-radians per Sample Hertz per second


   -1.0 -pi -Fs/2 -pi*Fs
   -0.5 -pi/2 -Fs/4 -pi*Fs/2
    0.0 0 0 0
    0.5 pi/2 Fs/4 pi*Fs/2
    1.0 pi Fs/2 pi*Fs



Key Formulas for Conversion:

  phi = alpha*pi

  f = alpha*Fs/2

  omega = 2*pi*f



Additional formulas (derived from above):

  f = phi*Fs/(2*pi)

  omega = alpha*pi*Fs

  omega = phi*Fs




HTH.

Rick


"Maya " <fratz0la@hotmail.com> wrote in message
news:i0tats$o2k$1@fred.mathworks.com...
> Matlab explicitly states that:
> "All of the non-object oriented filter design functions operate with
> normalized frequencies. Convert frequency specifications in Hz to
> normalized frequency to use these functions. The Signal Processing Toolbox
> software defines normalized frequency to be in the closed interval [0,1]
> with 1 denoting π radians/sample. For example, to specify a
> normalized frequency of π/2 radians/sample, enter 0.5.
> To convert from Hz to normalized frequency, multiply the frequency in Hz
> by two and divide by the sampling frequency." --> f(norm) =
> f(Hz)*2/F(sampl)
> What I would like to ask is:
> Does that mean that, for example, in a Magnitude (dB) diagram in fvtool
> using freqz function, the normalized frequency in point labeled 1 on the
> horizontal axis (that is, =pi since 1 corresponds to pi as stated
> underneath the axis) corresponds to Herz frequency in this way: f(Hz) =
> F(sampl)*f(norm)/2 = 8192*pi/2 = 4096*pi Herz??
> (where F(sampl) = 8192 by default when ploting with the freqz function)

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