Question

Please provide a detail outlline on how you would calculate the SNR of a filtered audio signal after it has been filtered through a bandpass filter. As you would observe from the FFT some values above and below the cutoff frequencies went to zero. How would you take that into consideration to calucalte the snr value . Essentially the snr value would be better than before the signal was filtered.

Answer 1

Claculation of SNR (Signal to Noise ratio) depends on what we consider to be `signal' (of interest) and what we consider to be unwanted `noise'. We need to somehow separate the signal and noise components using some a-priori information about their characteristics.

There are a number of techniques of estimation of SNR . There are some techniques are mentioned below to give and idea of SNR calculation

A) if we aware about the noise characteristics of the channel, and which is independent of the signal presence or absence, we could measure the noise power alone, then determine the SNR by the difference and ratio of the measurement in the presence of the signal.

SNR ={ ( Psig+noise) - Pnoise )} / Pnoise

B) If we know that the signals of inerest are pure tones(sinusoids), we could consider the power spectral density of the audio record. If we identify clearly the impulses in the PSD spectrum (This represents the signal , See figure), and, likely, the remaining part of the PSD is the scalled noise-floor. This can provide us sufficient information to calculate the noise power and signal power, again, their ratio gives SNR. This method (depends on the exact spectral characteristics) is suitable for wide band audio signals.

S tam

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Effect of filtering on SNR value

Filtering is done to reduce the presence of Noise and improve Signal to Noise Ration (SNR)

1. If high frequency noise signals are available , the low pass filter is used to improve SNR

2. If low frequency noise is there , the high pass filter helps to reduce noise and improve SNR value

3. In cas of band pass filtering noise signal of a specified frequency range is removed and specific range of signal passed through. That helps in improving SNR

This is a wrong assumption that SNR value would be better before filtering, as filtering is a concept (tool) to separate signal of interest from a mixture of signal and unwanted noise .A wise selection of filter helps in improving SNR .