# Relationship between noise power, SNR and bandwidth

• 17-04-07, 15:59
amlangford
snr and bandwidth parameters
Could somebody please explain the relationship between noise power (dBc/Hz), Bandwith (Hz) and SNR for a linear system.

Note: the noise power is quoted as a negative number

Thanks

• 17-04-07, 16:21
hurrynarain
relation between snr and bandwidth
your question is vague. try rephrasing it.

P.S:
Are you looking for shannon's channel capacity theorem?
• 17-04-07, 16:57
amlangford
bandwith snr
Sorry, ill rephrase my question.

Im working on some software that takes an audio input from the PC line input and applies gaussian noise of a given power to acheive a desired SNR, then passes the output to the soundcard line output.

A calibration routine measures the input signal power. The bandwidth is set by a filter on the soundcard output.

On the software interface are three parameters intrinsically related, these being bandwidth, SNR and noise power. Changing one alteres the other two.

Thus Im trying to understand the relationship between these parameters.

Hope this clarifies my question.

On an separate note, I am also slightly thrown by a reference in literiture Im reading that suggests that a 6dB difference exists between a "coherent" signal source and an "incoherent" noise source.

I think the term coherence used here is referring to in time i.e. a coherent signal source has strong correlation at time intervals, whereas a true noise source is always uncorrelated and thus incoherent.

Is my understanding of the (in)chorent term correct and any explanation of the 6dB difference???

Thank you
• 18-04-07, 07:52
hurrynarain
Re: Relationship between noise power, SNR and bandwidth
Let,

Signal Bandwidth - B_S
Noise Bandwidth - B_N
Filter Bandwidth - B_F

Power:
Signal : P_S (Over its Bandwidth B_S)
Noise : P_N (Over its Bandwidth B_N)

Noise varies with frequency (in case of Coloured Gaussian).

Effect of Changing one on the other:

1) Bandwidth:

As Bandwith is reduced to say B_F1 both signal and Noise power will reduce as power above B_F1 is reduced to zero.

Hence Signal power, Noise power will reduce and hence SNR would also vary (increase or decrease).

2) Noise Power :

As Noise Power is reduced to say P_N1 some of the noise signal would reduce effectively zeroing its power within the bandwidth.

Thus apart from Increasing SNR on reducing Noise power, it would reduce even the bandwidth (never increase on reducing noise power).

3) Signal Power:

Signal Power follows same explanation of noise power too.

bye.

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