Frequency Independent Phase Shifter

Electric guitar accessories shops sell "phasers". Nothing to do with the starship Enterprise.

Your fond of that stuff also Murphy? Wow..like shredding stuff? Awesome!

Of course not.

The Enterprise's phasers are way bigger.

regards,

Vulcan

Here are some ideas on the subject:

http://www.edaboard.com/thread244565.html

Lots of complicated stuff in that link. My Vulcan training hasn't reached that far.

I'll bookmark the website and go over it a little more carefully and get some ideas. Thanks.

regards,

Vulcan

I'm thinking that it is not possible. Suppose you take the Fourier Transform of the signal. This gives you a complex (real and imaginary) frequency function representation of the signal. A property of the Fourier Transform is that if you start with a completely real function (as in this case), that the frequency domain will have a real part that is even and an imaginary part that is odd. The converse is also true: if the real part is not an even function and the imaginary part is not an odd function, when you do a inverse Fourier Transform, the signal will not be completely real (it will be complex).

An even function of x has the same value for plus or minus x, i.e., f(x)=f(-x). For an odd function, f(x) = -f(-x). So the even real part will be symmetrical about the vertical axis. For the odd imaginary part, the negative side will be inverted from the positive side.

Now if you phase shift all the frequencies by 90 degrees, what happens is that for each component in the complex frequency spectrum, the +real part becomes imaginary, the imaginary part becomes -real, the -real becomes -imaginary, and the -imaginary becomes +real. Basically, for any frequency, the complex frequency gets rotated 90 degrees.

So if you phase shift all frequencies by 90 degrees, you are swapping the real and imaginary components in the frequency spectrum. So now, the real part is odd and the imaginary part is odd. So you cannot perform the inverse Fourier transform to obtain a real time function.

Oh wow, I studied to be an electronic service technician learning how to repair TVs and stereos. I was never introduced to Mr. Fourier, unfortunately, though I keep hearing about him from time to time.

From my searches, I kinda figured it's not possible with analog circuits but there might be someone who's done it. I don't want to spend too much time and money on experimenting.

For now, the only way I could think of doing it is via software; digitizing the audio signal and manipulating it in software to produce the 90° shift and reconverting it into an analog signal. The only thing holding me back is the processing power and memory I need to do that since I don't want it to get too expensive.

regards,

Vulcan

I'm thinking that it is not possible. Suppose you take the Fourier Transform of the signal. This gives you a complex (real and imaginary) frequency function representation of the signal. A property of the Fourier Transform is that if you start with a completely real function (as in this case), that the frequency domain will have a real part that is even and an imaginary part that is odd. The converse is also true: if the real part is not an even function and the imaginary part is not an odd function, when you do a inverse Fourier Transform, the signal will not be completely real (it will be complex).

An even function of x has the same value for plus or minus x, i.e., f(x)=f(-x). For an odd function, f(x) = -f(-x). So the even real part will be symmetrical about the vertical axis. For the odd imaginary part, the negative side will be inverted from the positive side.

Now if you phase shift all the frequencies by 90 degrees, what happens is that for each component in the complex frequency spectrum, the +real part becomes imaginary, the imaginary part becomes -real, the -real becomes -imaginary, and the -imaginary becomes +real. Basically, for any frequency, the complex frequency gets rotated 90 degrees.

So if you phase shift all frequencies by 90 degrees, you are swapping the real and imaginary components in the frequency spectrum. So now, the real part is odd and the imaginary part is odd. So you cannot perform the inverse Fourier transform to obtain a real time function.

I would like to disagree with Rixter . He should rotate around the positive frequency axis one way and around the negative frequency axis the other way (as seen from, say, the positive end), leaving the DC component alone. That way the odd imaginary component becomes the even real component and even real component becomes the odd imaginary component. Now when you do the inverse FFT you have a purely real time series with all components shifted 90 degrees.

If you have a short duration signal (< FFT size), you're good to go. If you have a continuous signal and you try to process it in blocks, you will have the usual problem with frequency domain processing, i.e., discontinuities between blocks. One way around this is to process in blocks overlapped by 50% and Hann weighted. This won't be perfect, but it should be pretty close.

Interesting!

The book says it will work but where do the A, B, C, D at the bottom go? Ground? The book doesn't say.

It is a strange and interesting-looking circuit, isn't it? The A B C D connections loop around to the top nodes marked A B C D, so the circuit cries out to be drawn as a cylindrical 3D object.

Four phase-sequence-filter nodes are marked 0°, 90°, 180° and 270°, and the four phase outputs are obtained as voltage differences between these nodes. So, as I mentioned, a difference amplifier (instrumentation amplifier) or transformer is required to finish the circuit. In our new 3rd-edition we rewrote this section, improved the circuit, added detailed performance plots, and gave a more clear description.

Double-sideband reduced-carrier quadrature-amplitude-modulation?

Oops, Winfield. Had it right...scratch QAM...replace with Phase Locked Quadrature Modulation.

Use a good AGC stage after shifting. Also using more than one RC stage for the shifting, would give a little less lousy performance. S.M.

A simple tube/valve or transistor circuit will produce 180 degree phase shift, there are also circuits that will provide 90 degrees of phase shift.

The circuit I think you are referring to, made with an RC and a unity-gain phase splitter (AoE 2nd ed Figs 2.28 to 2.30, and 3rd ed Figs 2.36 to 2.38), provides a 90° phase shift at only one frequency. But it does allow for a continuously-adjustable phase change, and it has the attractive property of maintaining a constant amplitude (at this fixed frequency) as you change the phase (a simple RC would change both the phase and the amplitude). If you adjust it to 90° at one frequency, the phase will change if you change the frequency. So basically, it's a single-frequency sine-wave phase changer.

The phase shifter in my first post is not continuously adjustable in phase, having fixed 0°, 90°, 180° and 270° outputs, but it works over many octaves of frequency, with nearly-constant amplitude. Note: it's a phase-difference circuit, so to use it an output transformer or differential-amplifier stage is required.

A discrete all-pass filter will give you your desired phase shift with in the pass band!!

A simple inverter will give you 180* phase shift at all pass band frequencies.... I'm sure there is a simple analogue method to do what you require.

John.

An analog Bessel filter has minimum phase shift versus frequency.