Sine Waves in Lossless?

bernardo · January 2008

Phasearray wrote: »

Nice write up! I admit that I need to go back and read my DSP stuff. Haven't touched the stuff since I graduated several years ago. so what do you have against Nyquist?

Well thank you. Glad you liked it

Nothing against Nyquist. In fact, that is how I learned it. But some people call it differently...

Phasearray wrote: »

My shallow understanding of DSP from an undergrad level is,

Correlation - comparing two signals. If you have two identical signals and you correlate them, the result is the maximum applitude, this is also refer to as the match filter. If you have two very different signals and you correlate them, the result is a very low signal. So when you correlate two signals and the result is a high amplitude, you can say that the two signals are faily alike or very different of the resulting amplitude is low.

Fourrier Transform - Concept is fairly easy to understand. Suppose I've sampled a single frequency signal. I have no idea what frequency it is. To figure out the frequency of the signal I "correlate it to other frequencies" Suppose I'm sampling a 1KHZ sine wave. When I correlate it to a 1 hz, 200 hz, and 5KHZ sine wave, the resulting amplitude is low. When I correlate that 1Khz Sinewave to another 1Khz sine wave or something close (999 Hz, 1001 Hz, etc) the resulting amplitude is high. This process of comparing my signal to a bunch of different frequencies is call fourrier transform. Fast Fourrier Transform(FFT) is just a computer optimized way of doing this.

The problem with the Digital Fourrier Transform is that I can't compare my sampled signal to every single HZ in existance. There's only a finite amount of comparisons I can do. If I sample a 990 Hz signal and correlate it to 1Khz, then I'll suffer some correlation lost here. I hate saying this because I don't know if I remember this correctly, bu I believe this is the limitation of doing a N-Point transform?

I never though of it as correlation (one of the reasons being that correlations has always carried mostly a stochastic meaning to me, although you can compute thecorrelation between 2 deterministic signals), just as projecting. As you would obtain x,y,z components of a vector in space. Correlation is quite close though, if I recall the math expressions to compute the Fourier coefficients and the one for correlation correctly (as far as I remember, correlation was very similar to a convolution with a sign difference at least)

And yes, the DFT (and hence the FFT) and signal pair are discrete and periodic in both time and frequency. That is one of the reasons why you can put it in a very nice matrix form and develop nice algorithms to compute it such as the FFT

But anyway, I don't think it was an issue for jakelm to find if he had a sampled sinusoid just how good a lossy-compressed one could be

Other than that, if you correlate a signal with something very similar you'll get a large correlation. As an example, if you correlate a rectangular pulse with itself, I'm pretty confident that you get a triangle of twice the width.

But, hey it's been a long time for me too

jakelm · January 2008

Pics please.....:p

Sine Waves in Lossless?

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