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vrf Zoom FFT

Question asked by fukui.yutaka on May 24, 2004

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Hi,

I heared about it at the seminar on the FFT held by the

National Instrument and feel a litle interest in it.

However, I have neither documentations nor examples (in VEE or C/C++)
about

the zoom FFT algorithm.

Regards,
FUKUI Yutaka

> Hello,
>
> Has anybody documentation or examples (in VEE or C/C++) about the zoom FFT algorithm implementation?
> I can't get enough information about it on internet.
>
> Thanks in advance,

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* $B$b$N$E$/$j?d?JKIt!&@8;:5;=Q3+H/E}3gIt!K7WB,@_Hw3+H/It (B
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* $B@n:j;TCf866h>e>.EDCf#4 (B- $B#1 (B- $B#1!!M9JXHV9f!' (B211-8588
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freal May 20, 2004 4:19 AM
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VRFuser May 23, 2004 6:18 PM
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Hello All,

With regard to the 'zoom FFT', I am not sure what NI are referring to exactly. There are many different forms of the Fourier Transform in wide use (discrete Fourier transform, chirp-Z transform and of course the FFT). In VEE-land, the FFT is relatively simple in that it takes real-valued 'time' data and its implementation of the FFT produces complex valued frequency domain data. VEE's native Fourier Transform does not allow you to input complex time domain data into the transform. However, the Matlab implementation of the FFT can employ real or complex valued time domain data. It may be that what NI are referring to is something similar to the Matlab FFT implementation.

In several HP/Agilent Signal Analyzer products, we have signal analysis (FFT) modes called 'baseband' and 'zoom'. In baseband mode, the frequency analysis region is from DC to some upper frequency. The sampled input time domain data is real. In zoom mode, an IQ demodulator is used to resolve a signal centred at some frequency Fo, into I and Q components. The FFT operates using I[n]+jQ[n], where n is the nth sample i.e. complex data into the FFT. The frequency domain analysis region then exists over some finite span about Fo, (span determined by the sampling rate).

Thus, if this is the type of capability you are looking for, then you can simply use Matlab's FFT with complex input data. Alternatively, Matlab also implements the Chirp-Z transform, which essentially allows you to analyzer specific regions in the frequency domain (within the sampling criteria established by Nyquist et al), with a user defined frequency increment.

If you can supply more info on exactly what you mean with zoom FFT, then it may be possible to identify either a native VEE function or Matlab function that will fulfil the requirement.

Hope this helps

Andy

-----Original Message-----
From: FUKUI Yutaka [mailto:fukui.yutaka@jp.fujitsu.com]
Sent: 24 May 2004 07:20
To: PDL-LISTS,VRF (A-Lists,unix1)
Subject: [vrf] Re:Zoom FFT

Hi,

I heared about it at the seminar on the FFT held by the

National Instrument and feel a litle interest in it.

However, I have neither documentations nor examples (in VEE or C/C++)
about

the zoom FFT algorithm.

Regards,
FUKUI Yutaka

> Hello,
>
> Has anybody documentation or examples (in VEE or C/C++) about the zoom FFT algorithm implementation?
> I can't get enough information about it on internet.
>
> Thanks in advance,

--
*****************************************************************
* $BJ!0f!!K-!J (JFUKUI Yutaka)
* E-Mail: fukui.yutaka@jp.fujitsu.com
* $BIY;NDL3t<02q<R!!@n:j9)>l (J
* $B$b$N$E$/$j?d?JKIt!&@8;:5;=Q3+H/E}3gIt!K7WB,@_Hw3+H/It (J
* $B7WB,@_Hw3+H/It (JHomePage http://www.psl.fujitsu.co.jp/htd2/ksk/
* $B@n:j;TCf866h>e>.EDCf#4 (J- $B#1 (J- $B#1!!M9JXHV9f!' (J211-8588
* TEL $B!!30@~ (J 044-754-3657, $B!!Fb@~ (J 711-3-1966,7
* FAX $B!!30@~ (J 044-754-3509, $B!!Fb@~ (J 711-3-5359
*****************************************************************

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bill.ossmann May 23, 2004 7:48 PM
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OK, thanks for the reference. It says quite clearly that the Zoom FFT is
not the same as the chirp Z-Transform.

To expand on their example a bit: ... if you have a sample rate of 10 MHz
and require at least 10Hz resolution over a small frequency band (say 1
KHz) then you do not need a 1 Mega point FFT, just decimate by a factor of
4096 and use a 256 point FFT which is obviously quicker.

If you have such a signal, it will be sampled at at least 20MHz to satisfy
the Nyquist criterion for a 10MHz signal. If the signal has 1kHz of
bandwidth it will be at least 1msec long or at least 20ksamples, more
likely longer if there is any structure within that 1kHz bandwidth. In any
case, if you want 10Hz resolution, you have to feed a 100msec signal into
your FFT, which amouts to 2Msamples in this case. Having done the FFT, you
only care about 100 points or so around 10MHz and ignore the rest, which
seems like a lot of wasted computation.

If you look at the Zoom FFT block diagram on the referenced page, you see
that by multiplying the original signal by exp(j*2*pi*(10MHz)*t) you shift
the spectrum down to a center of 0Hz, and an image at 20MHz (or its alias
if the sampling rate is less than 40MHz.) The FIR (finite impulse response)
filter is a low pass design to filter out this image, and in the DSP
hardware it probably is implemented in the time domain with just a few
taps. I don't know what the computational efficiency in VEE would be. Now
you have a 1kHz wide signal centered at DC which requires a sampling rate
of only 2kHz to satisfy the Nyquist criterion. Getting the required 100msec
of signal duration for the required 10Hz resolution then requires only
about 200 points, which is satisfied by the 256 point FFT as they state.

The web page is written up as a DSP method, so the computational efficiency
will be different in software (VEE or Matlab) running on a general purpose
machine (PC). In particular, the FIR filter would be implemented in a
pipelined processor on the DSP chip, and the 10MHz modulating signal
probably would be a digital synthesizer looking up values in a ROM in real
time. As a practical matter, in VEE the complex multiplication can be done
by separating into two paths, one multiplying by cos(2*pi*f*t) and the
other by sin(2*pi*f*t), much as shown on the web page. Since the VEE FFT
only keeps the positive frequency part of the spectrum, you will have to do
some manipulation to get the negative frequency part. Matlab can do the
whole thing as a complex signal and you get the entire spectrum, except
that it starts at zero, and the negative frequencies are in the far end of
the array. The fftshift() function will rotate 0Hz to the center of the
array if that's more convenient.

Try out different methods of implementing it and compare to the brute force
2Msample method.

Regards,
--
Bill Ossmann
Philips Ultrasound
e-mail: bill.ossmann@philips.com
--------------------------------------------------------

Hello Andy,

What we need to do is an analysis of a narrow-band spectrum (500 KHz)
centered on an arbitrary center frequency, increasing the frequency
resolution on that bandwidth ( typically, we will have as input a 36 MHz
signal or N samples in time domain).

It seems that we want what you describe as "zoom mode", do you have some
example in C,VEE or matlab?

Regarding to the Z-transform, I found the following description on
http://www.numerix-dsp.com/zoomfft.html:
"The FFT calculates the FFT at N equally spaced points around the unit
circle in the z-plane, the chirp z-transform modifies the locations of
these points along a contour that can lie anywhere on the z-plane. In
contrast, the zoom-FFT uses digital down conversion techniques to localise
the standard FFT to a narrow band of frequencies that are centered on a
higher frequency. The chirp z-transform is often used to analyze signals
such as speech, that have certain frequency domain charactgeristics. The
zoom-FFT is used to reduce the sample rate required when analysing
narrowband signals - E.G. in HF communications".

I do not really know if I could use Z-Transform to increase the frequency
resolution of my signal, could I? which is the best approach?

Thanks in advance,

-----Mensaje original-----
De: STREET,ANDY (A-England,ex2) [mailto:andy_street@agilent.com]
Enviado el: lunes, 24 de mayo de 2004 10:18
Para: VRF
Asunto: [vrf] Re:Zoom FFT

Hello All,

With regard to the 'zoom FFT', I am not sure what NI are referring to
exactly. There are many different forms of the Fourier Transform in wide
use (discrete Fourier transform, chirp-Z transform and of course the FFT).
In VEE-land, the FFT is relatively simple in that it takes real-valued
'time' data and its implementation of the FFT produces complex valued
frequency domain data. VEE's native Fourier Transform does not allow you
to input complex time domain data into the transform. However, the Matlab
implementation of the FFT can employ real or complex valued time domain
data. It may be that what NI are referring to is something similar to the
Matlab FFT implementation.

In several HP/Agilent Signal Analyzer products, we have signal analysis
(FFT) modes called 'baseband' and 'zoom'. In baseband mode, the frequency
analysis region is from DC to some upper frequency. The sampled input time
domain data is real. In zoom mode, an IQ demodulator is used to resolve a
signal centred at some frequency Fo, into I and Q components. The FFT
operates using I[n]+jQ[n], where n is the nth sample i.e. complex data into
the FFT. The frequency domain analysis region then exists over some finite
span about Fo, (span determined by the sampling rate).

Thus, if this is the type of capability you are looking for, then you can
simply use Matlab's FFT with complex input data. Alternatively, Matlab
also implements the Chirp-Z transform, which essentially allows you to
analyzer specific regions in the frequency domain (within the sampling
criteria established by Nyquist et al), with a user defined frequency
increment.

If you can supply more info on exactly what you mean with zoom FFT, then it
may be possible to identify either a native VEE function or Matlab function
that will fulfil the requirement.

Hope this helps

Andy

-----Original Message-----
From: FUKUI Yutaka [mailto:fukui.yutaka@jp.fujitsu.com]
Sent: 24 May 2004 07:20
To: PDL-LISTS,VRF (A-Lists,unix1)
Subject: [vrf] Re:Zoom FFT

Hi,

I heared about it at the seminar on the FFT held by the

National Instrument and feel a litle interest in it.

However, I have neither documentations nor examples (in VEE or C/C++)
about

the zoom FFT algorithm.

Regards,
FUKUI Yutaka

> Hello,
>
> Has anybody documentation or examples (in VEE or C/C++) about the zoom
FFT algorithm implementation?
> I can't get enough information about it on internet.
>
> Thanks in advance,

--
*****************************************************************
* $BJ!0f!!K-!J (BFUKUI Yutaka)
* E-Mail: fukui.yutaka@jp.fujitsu.com
* $BIY;NDL3t<02q<R!!@n:j9)>l (B
* $B$b$N$E$/$j?d?JKIt!&@8;:5;=Q3+H/E}3gIt!K7WB,@_Hw3+H/It (B
* $B7WB,@_Hw3+H/It (BHomePage http://www.psl.fujitsu.co.jp/htd2/ksk/
* $B@n:j;TCf866h>e>.EDCf#4 (B- $B#1 (B- $B#1!!M9JXHV9f!' (B211-8588
* TEL $B!!30@~ (B 044-754-3657, $B!!Fb@~ (B 711-3-1966,7
* FAX $B!!30@~ (B 044-754-3509, $B!!Fb@~ (B 711-3-5359
*****************************************************************

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freal May 23, 2004 8:43 PM
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Hello Andy,

What we need to do is an analysis of a narrow-band spectrum (500 KHz) centered on an arbitrary center frequency, increasing the frequency resolution on that bandwidth ( typically, we will have as input a 36 MHz signal or N samples in time domain).

It seems that we want what you describe as "zoom mode", do you have some example in C,VEE or matlab?

Regarding to the Z-transform, I found the following description on http://www.numerix-dsp.com/zoomfft.html:"The FFT calculates the FFT at N equally spaced points around the unit circle in the z-plane, the chirp z-transform modifies the locations of these points along a contour that can lie anywhere on the z-plane. In contrast, the zoom-FFT uses digital down conversion techniques to localise the standard FFT to a narrow band of frequencies that are centered on a higher frequency. The chirp z-transform is often used to analyze signals such as speech, that have certain frequency domain charactgeristics. The zoom-FFT is used to reduce the sample rate required when analysing narrowband signals - E.G. in HF communications".

I do not really know if I could use Z-Transform to increase the frequency resolution of my signal, could I? which is the best approach?

Thanks in advance,

-----Mensaje original-----
De: STREET,ANDY (A-England,ex2) [mailto:andy_street@agilent.com]
Enviado el: lunes, 24 de mayo de 2004 10:18
Para: VRF
Asunto: [vrf] Re:Zoom FFT

Hello All,

With regard to the 'zoom FFT', I am not sure what NI are referring to exactly. There are many different forms of the Fourier Transform in wide use (discrete Fourier transform, chirp-Z transform and of course the FFT). In VEE-land, the FFT is relatively simple in that it takes real-valued 'time' data and its implementation of the FFT produces complex valued frequency domain data. VEE's native Fourier Transform does not allow you to input complex time domain data into the transform. However, the Matlab implementation of the FFT can employ real or complex valued time domain data. It may be that what NI are referring to is something similar to the Matlab FFT implementation.

In several HP/Agilent Signal Analyzer products, we have signal analysis (FFT) modes called 'baseband' and 'zoom'. In baseband mode, the frequency analysis region is from DC to some upper frequency. The sampled input time domain data is real. In zoom mode, an IQ demodulator is used to resolve a signal centred at some frequency Fo, into I and Q components. The FFT operates using I[n]+jQ[n], where n is the nth sample i.e. complex data into the FFT. The frequency domain analysis region then exists over some finite span about Fo, (span determined by the sampling rate).

Thus, if this is the type of capability you are looking for, then you can simply use Matlab's FFT with complex input data. Alternatively, Matlab also implements the Chirp-Z transform, which essentially allows you to analyzer specific regions in the frequency domain (within the sampling criteria established by Nyquist et al), with a user defined frequency increment.

If you can supply more info on exactly what you mean with zoom FFT, then it may be possible to identify either a native VEE function or Matlab function that will fulfil the requirement.

Hope this helps

Andy

-----Original Message-----
From: FUKUI Yutaka [mailto:fukui.yutaka@jp.fujitsu.com]
Sent: 24 May 2004 07:20
To: PDL-LISTS,VRF (A-Lists,unix1)
Subject: [vrf] Re:Zoom FFT

Hi,

I heared about it at the seminar on the FFT held by the

National Instrument and feel a litle interest in it.

However, I have neither documentations nor examples (in VEE or C/C++)
about

the zoom FFT algorithm.

Regards,
FUKUI Yutaka

> Hello,
>
> Has anybody documentation or examples (in VEE or C/C++) about the zoom FFT algorithm implementation?
> I can't get enough information about it on internet.
>
> Thanks in advance,

--
*****************************************************************
* $BJ!0f!!K-!J (JFUKUI Yutaka)
* E-Mail: fukui.yutaka@jp.fujitsu.com
* $BIY;NDL3t<02q<R!!@n:j9)>l (J
* $B$b$N$E$/$j?d?JKIt!&@8;:5;=Q3+H/E}3gIt!K7WB,@_Hw3+H/It (J
* $B7WB,@_Hw3+H/It (JHomePage http://www.psl.fujitsu.co.jp/htd2/ksk/
* $B@n:j;TCf866h>e>.EDCf#4 (J- $B#1 (J- $B#1!!M9JXHV9f!' (J211-8588
* TEL $B!!30@~ (J 044-754-3657, $B!!Fb@~ (J 711-3-1966,7
* FAX $B!!30@~ (J 044-754-3509, $B!!Fb@~ (J 711-3-5359
*****************************************************************

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