14 votes
Accepted

Compute SQNR (Signal to Quantization Noise Ratio)

The signal voltage is a sinusoid signal variant from $-V$ to $+V$, thus the RMS value $$V_{rms} = \frac{V}{\sqrt{2}} = \frac{2^N \Delta V / 2}{\sqrt{2}}$$ because $2V = 2^N\Delta V$ where $\Delta V$ ...
AlexTP's user avatar
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11 votes
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Quantization SNR of sine wave doesn't match 1.761 + 6.02 * Q

Some issues here: Your SNR formula only applies to full scale sine waves, your sine wave has -6dB amplitude so your SNR will be 6 dB lower The formula also implies rounding, not truncation, that's ...
Hilmar's user avatar
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10 votes
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Increasing SNR and Dynamic Range using Oversampling

OP clarified that the question in the comments as follows: If we ignore any modulation for now and assume that we are receiving pure tones plus the band limited noise and we try to improve the SNR in ...
Dan Boschen's user avatar
9 votes
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Correct way to add AWGN to a signal

Short answer 10*log(bw/fs) to take into account the oversampling operation because the awgn() function specifies the signal-to-...
AlexTP's user avatar
  • 6,595
7 votes
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MATLAB: Adding Noise with Regard to Signal to Noise Ratio (SNR) or EbNo?

These stuffs $E_s/N_0, E_b/N_0 \textrm{ and SNR}$ are convertible. \begin{align} E_s/N_0 &= E_b/N_0 + 10\log_{10}(k) \\ E_s/N_0 &= 10\log_{10}(T_{sym}/T_{samp}) + \mathrm{SNR} \end{align} ...
AlexTP's user avatar
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7 votes

Quantization SNR of sine wave doesn't match 1.761 + 6.02 * Q

I was doing quite a bit wrong, but the key thing that I was missing was the fact that the SNR needs to be calculated over the whole Nyquist spectrum instead of only looking at the peaks. This article ...
Tom Verbeure's user avatar
7 votes
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Matched filter reference signal

What you have ia not a matched filter at all but instead a correlation receiver which correlates the received $r(t)$ with the possible transmitted signals $s_1(t)$ and $s_2(t)$ (note no time-reversal) ...
Dilip Sarwate's user avatar
6 votes
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SNR After Multiplying Two Noisy Signals

The multiplication of the two noisy signal gives $$(x_1+n_1)(x_2+n_2)=x_1x_2+x_1n_2+x_2n_1+n_1n_2=x+n\tag{1}$$ with the desired signal $$x=x_1x_2\tag{1}$$ and the noise part $$n=x_1n_2+x_2n_1+...
Matt L.'s user avatar
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6 votes
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Help in understanding the formula of Signal-to-Noise-Ratio (SNR) - Part 1

$\mathsf{SNR}$ (signal-to-noise ratio) is a generic term whose value can be defined in different ways by different people, and as long as one states clearly what is meant by $\mathsf{SNR}$ in a ...
Dilip Sarwate's user avatar
6 votes

Increasing SNR and Dynamic Range using Oversampling

When referring to the SNR achieved by oversampling, we have to be careful in using the term "SNR". There are essentially two SNR's to consider: The SNR that is the signal-to-quantization-...
Envidia's user avatar
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6 votes
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Signal to Quantization Noise ratio concept

Give me an A! Give me a D! Give me a converter! What have we got? An A/D converter! Go Team! Let $X$ denote a standard Gaussian random variable with pdf $\phi(x)$ and complementary CDF $Q(x)$. Let $Y$ ...
Dilip Sarwate's user avatar
6 votes

$\frac{\mathbb{E}[P]}{\mathbb{E}[N]}$ vs. $\mathbb{E}\left[\frac{P}{N}\right]$

Would the definition be equally intuitively valid? No. Using the expectation operator $\mathbb{E}$ implies that both $P$ and $N$ are functions of time. The problem with the second definition is that $...
Hilmar's user avatar
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5 votes
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Relationship between $E_b/N_0$ and $\rm SNR$ with channel coding

The relationship between SNR and $E_b/N_0$ is independent of the code rate. Note that $E_b$ is the energy per data bit (not the coded bits), and $R_b$ is the (uncoded) data bit rate. As long as you ...
Matt L.'s user avatar
  • 90k
5 votes
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Value of power spectral density $N_0$ or effect of scaling bandwidth to SNR

The noise power continues to be $N_0/2$, independent of bandwidth. The reason is that the noise variance at the output of a filter with frequency response $H(f)$ is $$\sigma_n^2=\int_{-\infty}^\infty \...
MBaz's user avatar
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5 votes
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Calculating penalty to SNR for non-matched filter

Let's consider a received signal $$Y(t)=Ap(t)+N(t)\tag{1}$$ where $A$ is the information symbol (modeled as a random variable), $p(t)$ is the transmit pulse, and $N(t)$ is additive white Gaussian ...
Matt L.'s user avatar
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5 votes

How to detect continuous noise in audio call?

My recommendation would be to do the processing in the frequency domain as methods are available that can directly be used to approach your problem. In many cases, speech "quality" is related to the ...
applesoup's user avatar
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5 votes
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Would the ratio of Autocorrelation value and autocorrelation of noise for different data types be different? in Matlab

I am not really sure what you want to do so please comment and I will modify my answer. The case that $x$ and $u$ seems statistically identical is that $x$ is standard Gaussian random variable and $u$...
AlexTP's user avatar
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5 votes
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Conversion between Eb/N0 and SNR in spread-spectrum modulation like LoRa CSS?

Let's start by fixing a symbol rate $R_s$ symbols per second. To modulate $R_s$ symbols per second without ISI, Nyquist says that we need a bandwidth at least $BW_0=1/R_s$ Hz. With spread spectrum, ...
AlexTP's user avatar
  • 6,595
5 votes
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Radar Pulse Compression Gain (PCR)

The answer is yes but one has to specify $B_n$ properly to avoide possible confusions. In case if one uses a pulse compression, the bandwidth through which the receiver collects the noise will ...
kda's user avatar
  • 66
5 votes

Signal to Quantization Noise ratio concept

Thus, for a partial statistical characterization of the quantizer in terms of output signal-to-(quantization) noise ratio, we need only find the mean-square value of the quantization error Q. All ...
TimWescott's user avatar
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5 votes
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SQNR vs SNDR (with regards to Delta Sigma Modulation)

The difference is SNQR is the SNR due to quantization noise alone as a theoretical limit while SNDR (also referred to as SINAD) includes multiple distortion sources in addition to quantization. SINAD ...
Dan Boschen's user avatar
4 votes

Acoustic Scenarios With Negative SNR

I've heard rumors of covert acoustic room impulse response measurement being done during concerts. You would need the people in the room if you want to use the impulse response for artificial ...
Olli Niemitalo's user avatar
4 votes
Accepted

Does lowpass filtering and decimating improve SNR?

So, let's not forget what SNR is: it's a relation of powers present. The thing that improves SNR is a propoer low-pass: it leaves the signal power alone and reduces the power of the noise. An ideal ...
Marcus Müller's user avatar
4 votes
Accepted

Pulse Compression(Chirp) SNR Gain

It's often said that pulse compression gives you a gain proportional to the time-bandwidth product (otherwise known as the pulse compression ratio, or $PCR$). This is a really misleading statement, ...
Beepboop bebop's user avatar
4 votes
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Noise variance calculation for 16APSK Demodulator

This is to take into account the oversampling operation. Symbol time = sample time implies no oversampling. See AWGN model for more details about the conversion among EbN0, EsN0 and SNR. For ...
AlexTP's user avatar
  • 6,595
4 votes
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Downsampling impact on complex phase

Decimating a signal (selecting every Dth sample and discarding the rest) does not distort the signal within the passband in any way other than to cause aliases from higher frequencies to fold into the ...
Dan Boschen's user avatar
4 votes
Accepted

Optimal amplitude of an $m$-bit sinusoid

The phase of the sinusoid does not matter: A phase shift of a sinusoid is equivalent to shifting it in time, which results in a time shift of both the quantized sinusoid and the quantization error. ...
Olli Niemitalo's user avatar
4 votes
Accepted

Generate signals with a particular variance and SNR

It depends on what you mean by SNR. It's a common joke in the DSP community to spell it out as "something to noise ratio", referring to the fact that there is no unique definition of SNR, so the term ...
Florian's user avatar
  • 2,463
4 votes
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How many bins to include when calculating SNR from FFT?

The OP's question requires further details to provide a definitive answer, but the following will give the considerations involved. If the noise is white and stationary then the answer is clear in ...
Dan Boschen's user avatar
4 votes
Accepted

How is signal to noise ratio actually measured by receiver equipment?

The SNR is simply the mean-square of a demodulated symbol divided by the variance of the signal, or in dB: $$\DeclareMathOperator{\SNR}{SNR}\SNR =10\log_{10}(\mu^2/\sigma^2)$$ $$=20\log_{10}(\mu/\...
Dan Boschen's user avatar

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