engineering

Signal-to-quantization-noise ratio

Signal-to-quantization-noise ratio is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Signal-to-quantization-noise ratio rather than just read about it. In short: Signal-to-quantization-noise ratio (SQNR or SNqR) is widely used quality measure in analysing digitizing schemes such as pulse-code modulation (PCM). The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error (also known as quantization noise) introduced in the analog-to-digital conversion.

Key takeaways

Signal-to-quantization-noise ratio belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Signal-to-quantization-noise ratio to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Signal-to-quantization-noise ratio from memory before moving on to harder problems.

Reference excerpt

Signal-to-quantization-noise ratio (SQNR or SNqR) is widely used quality measure in analysing digitizing schemes such as pulse-code modulation (PCM). The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error (also known as quantization noise) introduced in the analog-to-digital conversion. As SQNR applies to quantized signals, the formulae for SQNR refer to discrete-time digital signals. Instead of the value- and time-continuous message signal m ( t ) {\displaystyle m(t)} , the digitized signal x ( n ) {\displaystyle x(n)} will be used. For N {\displaystyle N} quantization steps, each sample, x {\displaystyle x} requires ν = log 2 ⁡ N {\displaystyle \nu =\log _{2}N} bits. The probability distribution function (PDF) represents the distribution of values in x {\displaystyle x} and can be denoted as f ( x ) {\displaystyle f(x)} . The maximum magnitude value of any x {\displaystyle x} is denoted by x m a x {\displaystyle x_{max}} . As SQNR, like SNR, is a ratio of signal power to some noise power, it can be calculated as:

S Q N R = P s i g n a l P n o i s e = E [ x 2 ] E [ x ~ 2 ] {\displaystyle \mathrm {SQNR} ={\frac {P_{signal}}{P_{noise}}}={\frac {E[x^{2}]}{E[{\tilde {x}}^{2}]}}}

The signal power is:

x 2 ¯ = E [ x 2 ] = P x ν = ∫

x 2 f ( x ) d x {\displaystyle {\overline {x^{2}}}=E[x^{2}]=P_{x^{\nu }}=\int _{}^{}x^{2}f(x)dx}

The quantization noise power can be expressed as:

E [ x ~ 2 ] = x m a x 2 3 × 4 ν {\displaystyle E[{\tilde {x}}^{2}]={\frac {x_{max}^{2}}{3\times 4^{\nu }}}}

Giving:

S Q N R = 3 × 4 ν × x 2 ¯ x m a x 2 {\displaystyle \mathrm {SQNR} ={\frac {3\times 4^{\nu }\times {\overline {x^{2}}}}{x_{max}^{2}}}}

When the SQNR is desired in terms of decibels (dB), a useful approximation to SQNR is:

S Q N R | d B = P x ν + 6.02 ν + 4.77 {\displaystyle \mathrm {SQNR} |_{dB}=P_{x^{\nu }}+6.02\nu +4.77}

where ν {\displaystyle \nu } is the number of bits in a quantized sample, and P x ν {\displaystyle P_{x^{\nu }}} is the signal power calculated above. Note that for each bit added to a sample, the SQNR goes up by approximately 6 dB ( 20 × l o g 10 ( 2 ) {\displaystyle 20\times log_{10}(2)} ).

References B. P. Lathi, Modern Digital and Analog Communication Systems (3rd edition), Oxford University Press, 1998

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Signal-to-quantization-noise ratio

Start with the simplest possible case. Write down what Signal-to-quantization-noise ratio claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Signal-to-quantization-noise ratio before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Signal-to-quantization-noise ratio ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Signal-to-quantization-noise ratio

In research: Signal-to-quantization-noise ratio appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Signal-to-quantization-noise ratio in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Signal-to-quantization-noise ratio is common in secondary-school and first-year university syllabi. It links to neighbouring topics Digital audio, Engineering ratios, Noise (electronics), so understanding it makes those chapters shorter.
In everyday life: Look for Signal-to-quantization-noise ratio outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Signal-to-quantization-noise ratio in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Signal-to-quantization-noise ratio means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Signal-to-quantization-noise ratio out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Signal-to-quantization-noise ratio in simple terms?

Why does Signal-to-quantization-noise ratio matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Signal-to-quantization-noise ratio?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Signal-to-quantization-noise ratio.