I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the frequency band that i can use is below 4000Hz (8000/2). I would like to have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to 3kHz and 3kHz will go to 300Hz and the in-between are flip). I tried many methods to do it but fails. 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, there's distortion. 2) Like a SSB modulation, to move the lower band in the (300 to 3k) region. But it requires a Hilbert transform. There are many approximations of Hilbert transform like using remez function in matlab and other FIR or IIR filters. But in SSB, if the phase response of those filters are not out-of-phase 90 degree difference, the upper band components cannot be cancelled and the result is not good. So can anyone help me to figure out those problem or have any other good scrambling methods or algorithms that are easy to implement in DSP.

# Frequency Inversion

Started by ●August 28, 2006

Reply by ●August 28, 20062006-08-28

bachbeethoven200 wrote:> I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > frequency band that i can use is below 4000Hz (8000/2). I would like to > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > > I tried many methods to do it but fails. > > 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) > that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, > there's distortion. >If you are going to mix one signal with another to get a desired output, you will need to put a filter on your output to remove the unwanted signal component. Recall that cosA * cosB = cos( A + B ) + cos( A - B ). So if you only want the lower component you would need a lowpass filter with the proper cutoff frequency.> 2) Like a SSB modulation, to move the lower band in the (300 to 3k) > region. But it requires a Hilbert transform. There are many approximations > of Hilbert transform like using remez function in matlab and other FIR or > IIR filters. But in SSB, if the phase response of those filters are not > out-of-phase 90 degree difference, the upper band components cannot be > cancelled and the result is not good. > > So can anyone help me to figure out those problem or have any other good > scrambling methods or algorithms that are easy to implement in DSP.

Reply by ●August 28, 20062006-08-28

On Mon, 28 Aug 2006 05:24:19 -0500, "bachbeethoven200" <beethoven@wyk.edu.hk> wrote:>I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the >frequency band that i can use is below 4000Hz (8000/2). I would like to >have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to >3kHz and 3kHz will go to 300Hz and the in-between are flip). > >I tried many methods to do it but fails. > >1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) >that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, >there's distortion. > >2) Like a SSB modulation, to move the lower band in the (300 to 3k) >region. But it requires a Hilbert transform. There are many approximations >of Hilbert transform like using remez function in matlab and other FIR or >IIR filters. But in SSB, if the phase response of those filters are not >out-of-phase 90 degree difference, the upper band components cannot be >cancelled and the result is not good. > >So can anyone help me to figure out those problem or have any other good >scrambling methods or algorithms that are easy to implement in DSP.Hi bachbeethoven, I can't think of a simple way to invert your spectrum that doesn't require quadrature processing (complex-valued samples) or frequency-domain processing (performing forward and inverse DFTs). However, you might take your original real-valued time sequence and negate (change the sign) of alternate samples. That will give you an inverted spectrum positioned from 1000 -to- 3700 Hz. That's not exactly what you asked for, but maybe it could somehow be used in your application. Good Luck, [-Rick-]

Reply by ●August 28, 20062006-08-28

bachbeethoven200 wrote:> I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > frequency band that i can use is below 4000Hz (8000/2). I would like to > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > > I tried many methods to do it but fails. >All you have to do is invert the sign of the every second sample.> 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) > that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, > there's distortion. > > 2) Like a SSB modulation, to move the lower band in the (300 to 3k) > region. But it requires a Hilbert transform. There are many approximations > of Hilbert transform like using remez function in matlab and other FIR or > IIR filters. But in SSB, if the phase response of those filters are not > out-of-phase 90 degree difference, the upper band components cannot be > cancelled and the result is not good.:)))) In many cases, extra knowledge is only harmfull.> So can anyone help me to figure out those problem or have any other good > scrambling methods or algorithms that are easy to implement in DSP.Take any voice compression algorithm (like G.723.1 for example) and apply AES to the digital data. Keep in mind that the development of such algorithms is a controlled issue in most of the countries. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com

Reply by ●August 28, 20062006-08-28

"bachbeethoven200" <beethoven@wyk.edu.hk> writes:> I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > frequency band that i can use is below 4000Hz (8000/2). I would like to > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > > I tried many methods to do it but fails. > > 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) > that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, > there's distortion. > > 2) Like a SSB modulation, to move the lower band in the (300 to 3k) > region. But it requires a Hilbert transform. There are many approximations > of Hilbert transform like using remez function in matlab and other FIR or > IIR filters. But in SSB, if the phase response of those filters are not > out-of-phase 90 degree difference, the upper band components cannot be > cancelled and the result is not good. > > So can anyone help me to figure out those problem or have any other good > scrambling methods or algorithms that are easy to implement in DSP.I don't mean to frustrate you (I know I am sometimes frustrated when people ask me these types of questions), but perhaps it would help to know WHY you want to perform this operation. Perhaps there is another approach to your problem altogether that is simpler. -- % Randy Yates % "Though you ride on the wheels of tomorrow, %% Fuquay-Varina, NC % you still wander the fields of your %%% 919-577-9882 % sorrow." %%%% <yates@ieee.org> % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr

Reply by ●August 28, 20062006-08-28

bachbeethoven200 wrote:> I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > frequency band that i can use is below 4000Hz (8000/2). I would like to > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > > I tried many methods to do it but fails. > > 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) > that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, > there's distortion. > > 2) Like a SSB modulation, to move the lower band in the (300 to 3k) > region. But it requires a Hilbert transform. There are many approximations > of Hilbert transform like using remez function in matlab and other FIR or > IIR filters. But in SSB, if the phase response of those filters are not > out-of-phase 90 degree difference, the upper band components cannot be > cancelled and the result is not good. > > So can anyone help me to figure out those problem or have any other good > scrambling methods or algorithms that are easy to implement in DSP. >I think that one way or another you're going to be implementing a Hilbert transform, or at least replicating the amount of delay and computational complexity of using it. Are you band-limiting your Hilbert transform? A true Hilbert transform with a response that goes down to DC has an infinite height in the time domain, which can be a bit rough to implement with real components. But if you cascade a Hilbert transform with a high-pass filter the response is large, but not infinite. You may want to consider, instead of using a delayed version of your signal and a hilbert transformed version, to use one version shifted +45 degrees, and another shifted -45. If nothing else this will ease the height of the peak by a factor of 2. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html

Reply by ●August 28, 20062006-08-28

Vladimir, Reading a little into the original post I would guess that he is trying to preserve the audio bandwidth to put the inverted audio through a bandlimited channel. If you have a spectrum from 300-3000 Hz (8Ksps) and flip every other sample as suggested, the inverted spectrum covers 1000-3700 Hz. Passing this through a channel that cuts off at 3000 Hz limits the inverted channel to 1000-3000 Hz. When this is inverted, the original frequency content is limited to 1000-3000 Hz which makes for some really bad audio. So inverting the sign of every other sample is not the way to go. Dirk Bell DSP Consultant Vladimir Vassilevsky wrote:> bachbeethoven200 wrote: > > > I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > > frequency band that i can use is below 4000Hz (8000/2). I would like to > > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > > > > I tried many methods to do it but fails. > > > > All you have to do is invert the sign of the every second sample. > > > > 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) > > that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, > > there's distortion. > > > > 2) Like a SSB modulation, to move the lower band in the (300 to 3k) > > region. But it requires a Hilbert transform. There are many approximations > > of Hilbert transform like using remez function in matlab and other FIR or > > IIR filters. But in SSB, if the phase response of those filters are not > > out-of-phase 90 degree difference, the upper band components cannot be > > cancelled and the result is not good. > > :)))) > In many cases, extra knowledge is only harmfull. > > > > So can anyone help me to figure out those problem or have any other good > > scrambling methods or algorithms that are easy to implement in DSP. > > Take any voice compression algorithm (like G.723.1 for example) and > apply AES to the digital data. Keep in mind that the development of such > algorithms is a controlled issue in most of the countries. > > > Vladimir Vassilevsky > > DSP and Mixed Signal Design Consultant > > http://www.abvolt.com

Reply by ●August 28, 20062006-08-28

Musicman, Stick with the SSB approach. Process should be complex mix, lowpass filter, complex mix, take real part to get the audio inverted around 1650 Hz (last 2 steps can be combined for simplicity). Work through this on paper to make sure everything is going where you expect it to go spectrally, and with a little more work you will see how to invert it. The quality can be very good, I have done it this way. Dirk Bell DSP Consultant bachbeethoven200 wrote:> I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > frequency band that i can use is below 4000Hz (8000/2). I would like to > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > > I tried many methods to do it but fails. > > 1) Like a frequency shifting, I can shift the (-3k to 300) to (300 and 3k) > that means multipy a cosine of 3300Hz, but due to the 8000 sampling rate, > there's distortion. > > 2) Like a SSB modulation, to move the lower band in the (300 to 3k) > region. But it requires a Hilbert transform. There are many approximations > of Hilbert transform like using remez function in matlab and other FIR or > IIR filters. But in SSB, if the phase response of those filters are not > out-of-phase 90 degree difference, the upper band components cannot be > cancelled and the result is not good. > > So can anyone help me to figure out those problem or have any other good > scrambling methods or algorithms that are easy to implement in DSP.

Reply by ●August 29, 20062006-08-29

bachbeethoven200 wrote:> I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > frequency band that i can use is below 4000Hz (8000/2). I would like to > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > 3kHz and 3kHz will go to 300Hz and the in-between are flip)....> So can anyone help me to figure out those problem or have any other good > scrambling methods or algorithms that are easy to implement in DSP.I always thought that scrampling signals that way (frequency inversion) or by permuting frequency bands was only used for analog signals. For digital signals, it would seem that standard data encryption is a) much more secure and b) simpler to implement. VLV mentioned AES, which would also be my algorithm of choice. There is source code out there, just look. Regards, Andor

Reply by ●August 29, 20062006-08-29

Andor, Even if the signal is digitized for processing (which may be required for the scrambler implementation chosen) , the signal may have to be converted back to analog to go through a low bandwidth analog channel (analog telephone channel, analog radio channel). I ran into this general type of frequency inversion in production in 2002. Dirk Bell DSP Consultant Andor wrote:> bachbeethoven200 wrote: > > I have an audial signal of sampling rate 8000Hz (16 bits per sample) so the > > frequency band that i can use is below 4000Hz (8000/2). I would like to > > have a frequency inversion of 300Hz to 3kHz that means (300Hz will go to > > 3kHz and 3kHz will go to 300Hz and the in-between are flip). > ... > > So can anyone help me to figure out those problem or have any other good > > scrambling methods or algorithms that are easy to implement in DSP. > > I always thought that scrampling signals that way (frequency inversion) > or by permuting frequency bands was only used for analog signals. For > digital signals, it would seem that standard data encryption is a) much > more secure and b) simpler to implement. > > VLV mentioned AES, which would also be my algorithm of choice. There is > source code out there, just look. > > Regards, > Andor