Sirs, I have few questions on the characteristic of noise when it comes to processing signals with noise: 1) does it really matter what is the shape of a noise - ramp, triangle, sinusodal etc. 2) does it really matter that they very unlikely to be periodic Thanks, Manish
noise
Started by ●December 23, 2012
Reply by ●December 23, 20122012-12-23
On Sunday, December 23, 2012 8:14:23 AM UTC-6, manishp wrote:> Sirs, > > > > I have few questions on the characteristic of noise when it comes to > > processing signals with noise: > > > > 1) does it really matter what is the shape of a noise - ramp, triangle, > > sinusodal etc. > > 2) does it really matter that they very unlikely to be periodic > > > > Thanks, Manish1) What do _you_ mean by the _shape_ of a noise? 2) Yes and No
Reply by ●December 23, 20122012-12-23
"manishp" <58525@dsprelated> writes:> Sirs, > > I have few questions on the characteristic of noise when it comes to > processing signals with noise: > > 1) does it really matter what is the shape of a noise - ramp, triangle, > sinusodal etc. > 2) does it really matter that they very unlikely to be periodic > > Thanks, ManishManish, As Dilip intimated, you need to be more clear about the term "noise." In the colloquial sense, noise is anything that interferes with communication. If you use the term noise in a room full of communications and signal processing engineers, they will however think you are speaking of a "random signal," i.e., a signal that can be described as a "random process," and thus will speak of things like ergodicity, stationarity, autocorrelation, power spectral desnity, etc. In the precise field of communications, a sine wave (or ramp or triangle wave, or any deterministic signal) is not considered "noise." There is another term used for such things: "interference." And there are distinctly different methods used to deal with interference versus noise. Your question isn't very clear to me. Perhaps if you told us the reason or motive behind your question? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●December 23, 20122012-12-23
manishp wrote:> Sirs, > > I have few questions on the characteristic of noise when it comes to > processing signals with noise: > > 1) does it really matter what is the shape of a noise - ramp, triangle, > sinusodal etc. > 2) does it really matter that they very unlikely to be periodic > > Thanks, Manish >There is error. you can divide error into noise and distortion. Noise is uncorrelated. Distortion is correlated. -- Les Cargill
Reply by ●December 23, 20122012-12-23
Randy Yates <yates@digitalsignallabs.com> wrote: (snip)> If you use the term noise in a room full of communications and signal > processing engineers, they will however think you are speaking of a > "random signal," i.e., a signal that can be described as a "random > process," and thus will speak of things like ergodicity, stationarity, > autocorrelation, power spectral desnity, etc.> In the precise field of communications, a sine wave (or ramp or triangle > wave, or any deterministic signal) is not considered "noise." There is > another term used for such things: "interference." And there are > distinctly different methods used to deal with interference versus > noise.Well, that would be true if you knew the signal (frequency, phase, amplitude) well enough to subtract it. If not, then it might as well be noise.> Your question isn't very clear to me. Perhaps if you told us the > reason or motive behind your question?Consider a recording with ground loop 60Hz added to it. Assume for now no non-linear effects, so no harmonics. With some luck, you can phase lock to it, and subtract it out, but maybe not quite good enough. Seems like noise to me. -- glen
Reply by ●December 24, 20122012-12-24
Sirs, Thanks for your response. Let me try and elaborate ... Since generally noise can be random at best (both in terms of when & how it occurs), I am trying to understand how they can be defined ... Few specific questions below: 1) let us assume that the information is a pure sine wave and further assume noise is just one single point of a specific amplitude in a specific window. In this case, when the information gets corrupted by noise, will the resulting signal appear as a high frequency change in the original signal. Remember, the noise is just a single pulse ... 2) does noise always have an effect of adding to the signal (that is, signal +- noise) or they can be transformation of any other form? Thanks once again, manish
Reply by ●December 24, 20122012-12-24
On 12/24/2012 3:18 AM, manishp wrote:> Sirs, > > Thanks for your response. Let me try and elaborate ... > > Since generally noise can be random at best (both in terms of when& how it > occurs), I am trying to understand how they can be defined ... > > Few specific questions below: > 1) let us assume that the information is a pure sine wave and further > assume noise is just one single point of a specific amplitude in a specific > window. In this case, when the information gets corrupted by noise, will > the resulting signal appear as a high frequency change in the original > signal. Remember, the noise is just a single pulse ... > > 2) does noise always have an effect of adding to the signal (that is, > signal +- noise) or they can be transformation of any other form? > > Thanks once again, manishIf I understand what you are describing, this would be an impulse which has energy throughout the spectrum, not just at the high end. But I'm not sure what you mean by "in a specific window". Rick
Reply by ●December 24, 20122012-12-24
On Mon, 24 Dec 2012 02:18:47 -0600, "manishp" <58525@dsprelated> wrote:>Sirs, > >Thanks for your response. Let me try and elaborate ... > >Since generally noise can be random at best (both in terms of when & how it >occurs), I am trying to understand how they can be defined ... > >Few specific questions below: >1) let us assume that the information is a pure sine wave and further >assume noise is just one single point of a specific amplitude in a specific >window. In this case, when the information gets corrupted by noise, will >the resulting signal appear as a high frequency change in the original >signal. Remember, the noise is just a single pulse ...Remember that the Fourier Transform is linear, so superposition applies in both domains. In other words, when you add noise to a signal, the spectra of the two signals add, too. So in the frequency domain the spectrum of the sine wave is added to the spectrum of the added noise. The spectrum of the sine wave is a spike, and the spectrum of the impulse is broad and flat.>2) does noise always have an effect of adding to the signal (that is, >signal +- noise) or they can be transformation of any other form?Most noise is additive, but never assume that. A common noise model is AWGN, or Additive White Gaussian Noise. The first word "additive" is important because it clarifies that it is, in fact, an additive model. Usually noise is additive, but it can be important to clarify this to be sure in a particular context.>Thanks once again, manishEric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●December 25, 20122012-12-25
>Remember that the Fourier Transform is linear, so superposition >applies in both domains. In other words, when you add noise to a >signal, the spectra of the two signals add, too. So in the frequency >domain the spectrum of the sine wave is added to the spectrum of the >added noise. The spectrum of the sine wave is a spike, and the >spectrum of the impulse is broad and flat.Thank you very much. I do have a question on the spectrum of sine and impulse. Leaving the theory apart, intuitively (thinking in time and frequency terms) it is clear that spectrum of a sine wave is a pulse. But is is not intuitive how a spectrum of a impulse can spread across frequency spectrum. It is difficult to imagine that a point can contain multiple frequency terms although when we see the transform equation, it does make sense ... Thanks, Manish
Reply by ●December 25, 20122012-12-25
On 12/24/12 1:02 PM, Eric Jacobsen wrote:> On Mon, 24 Dec 2012 02:18:47 -0600, "manishp"<58525@dsprelated> > wrote: > >> Sirs, >> >> Thanks for your response. Let me try and elaborate ... >> >> Since generally noise can be random at best (both in terms of when& how it >> occurs), I am trying to understand how they can be defined ... >> >> Few specific questions below: >> 1) let us assume that the information is a pure sine wave and further >> assume noise is just one single point of a specific amplitude in a specific >> window. In this case, when the information gets corrupted by noise, will >> the resulting signal appear as a high frequency change in the original >> signal. Remember, the noise is just a single pulse ... > > Remember that the Fourier Transform is linear, so superposition > applies in both domains. In other words, when you add noise to a > signal, the spectra of the two signals add, too. So in the frequency > domain the spectrum of the sine wave is added to the spectrum of the > added noise. The spectrum of the sine wave is a spike, and the > spectrum of the impulse is broad and flat. > >> 2) does noise always have an effect of adding to the signal (that is, >> signal +- noise) or they can be transformation of any other form? > > Most noise is additive, but never assume that. A common noise model > is AWGN, or Additive White Gaussian Noise. The first word "additive" > is important because it clarifies that it is, in fact, an additive > model. Usually noise is additive, but it can be important to clarify > this to be sure in a particular context.contrast this with quantization noise. it actually is not strictly additive, but is a function of the signal getting quantized. but we model it as "additive" simply by defining it as the difference between the quantized signal and the pre-quantized signal. that makes it "additive". but it's still not independently added. if the signal swing is large and unrelated to the sampling frequency, this additive quantization noise starts appearing (or sounding) more independent and then it might be modeled as additive white (up to Nyquist) and uniform p.d.f. noise. but i don't think they call that "AWUN" or "AWRN" ("rectangular" p.d.f.). with the right kind of dither, it gets more uncorrelated and looks a little more gaussian. if you add triangular p.d.f. dither of 2 LSBs width, the quantization noise will be white and uncorrelated (first two moments) and the p.d.f. will be that from convolving the rectangular p.d.f. with itself twice. a piece-wise quadratic function that looks a little bit like gaussian. but still not precisely AWGN. but we might be tempted to start calling it that, just to make our lives easier. just another $0.02 -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
