Timeline for White Gaussian Noise Spectrum and Power
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2020 at 9:24 | comment | added | Marcus Müller | @Noha well said, but we need to be very careful here: You're mixing the terms of an energy spectrum of an observed signal with a finite length with a power spectral density, which is a stochastic property of an infinitely long weak-sense stationary process. If we apply the same methodology to both – saying "my signal exists only for my observation length, but I integrate over infinity and find the limit of integral divided by integration length", then all signals have 0 power everywhere. Don't mix these terms! | |
| Dec 9, 2020 at 9:19 | comment | added | Noha | The magnitude spectrum of Fourier transform tells us how much a certain frequency is found in a signal relative to the other frequencies found in that signal. If the frequency is not found, the magnitude spectrum at that spectrum is zero. If it is found (in the form of sinusoid) with small amplitude and limited duration, the magnitude spectrum at that frequency will be small. | |
| Dec 8, 2020 at 21:30 | comment | added | Marcus Müller | "composed of" is a dangerous term: composed of uncountably many weighted sinusoids? Sure, that's a sensible interpretation of what the Fourier transform is. Composed of a countable set of discrete sinusoids: No! Only infinitely long periodic signals are. | |
| Dec 8, 2020 at 21:21 | comment | added | Noha | I know that the spectrum of a limited sinusoid is a sinc-shaped, but this doesn't mean that it has power. Of course it has power. I think any signal is composed of different sinusoids with different durations and amplitudes. | |
| Dec 8, 2020 at 19:05 | comment | added | Marcus Müller | If you make the duration finite, you can no longer exactly be sure whether it was at a frequency $f_0$. In fact, by limiting your sinusoids "existence", you just windowed it with a rectangle – meaning the spectrum is now sinc-shaped, and no longer a dirac. | |
| Dec 8, 2020 at 14:08 | comment | added | Noha | I understand that mathematically, but I can not imagine that. A sinusoid always has power even if finite in duration, and of course every frequency is represented as a sinusoid with certain duration in the signal. | |
| Dec 8, 2020 at 13:30 | comment | added | Marcus Müller | We can define power at a single frequency. It's 0 for white noise. It's because an integral over a single point of a bounded function is always 0, see my comments under Mark's answer. | |
| Dec 8, 2020 at 13:30 | comment | added | Marcus Müller | $N_0$ vs $N_0/2$: complex or real signals; depends on your definition of bandwidth. So, watch out for how the texts define bandwidth. | |
| Dec 8, 2020 at 12:49 | comment | added | Noha | I need to understand the following: why we can't define power for a single frequency component, unless there is a sinusoid at that frequency? infinitely long periodic signals, e.g. sine waves, have power at a single frequency, but any signal consists of a range of frequencies in the form of sinusoidal signals. Each sinusoid has a certain duration in the signal. Infinitely long sinusoidal signals have power, and also finite sinusoidal signals have power. | |
| Dec 8, 2020 at 12:05 | comment | added | Noha | The power spectral density of AWGN is constant at No/2 or No? What I read is that it is constant at No/2, while the definition of No is the amount of power per unit bandwidth watt/Hz. Why No is divided by two? If we don't divide by two, then the value of the constant PSD is No (Watt/Hz), which when multiplied by the total bandwidth will give the total power. | |
| Dec 5, 2020 at 10:18 | history | answered | Marcus Müller | CC BY-SA 4.0 |