# What is meant by signal-to-noise ratio?

1. May 22, 2005

### nktvnvn

What is meant by "signal-to-noise ratio?"

What does it mean saying that the SNR of an audio system is 97dB? I'd be grateful for your explanation. Thanks.

2. May 23, 2005

3. May 23, 2005

### nktvnvn

Thanks for your help but because I don't understand what Wikipedia says, I turn to you guys for help.
Wikipedia's articles are informative but not necessarily easy to understand, you know.

4. May 23, 2005

### FredGarvin

Let's see if I can do this in easier terms...

In a signal there is going to be the actual signal that you are interested in. What ever that signal is is not really important. When you look at that signal, there will be other things there that you do not care about, but travel on the same source that you are observing. For example, lets say you are looking at the output signal of a transducer that monitors pressure. As the pressure increases, the signal output of the transducer will, for argument's sake, go up as well. When you look at the signal from the transducer on an o-scope, the signal will not be a perfect line...it will have other junk on it as well. You may have a generally straight line that indicates some voltage reading, but that line will be somewhat distorted, perhaps some peaks or some waviness to it. That distortion is the noise, the part of the signal you don't care about.

So when you are talking about signal to noise ratio, you are talking about a ratio of the good signal to the bad part of the signal. Obviously you want a high ratio. That means the relative strength of the good part is higher than the strength of the bad.

The resultant ratio is a number. Because the numbers involved, that ratio can swing dramatically between huge and small numbers. Because of that, the decibel is used as a measure. This is a way to mathematically reduce those huge numbers into something more manageable.

Since there are a lot of different source signals that one can be talking about, the shape of the signal can also have many different forms. Signals like sinusoidal, frequency spectrums, etc...it's not limited to the straight line I had mentioned.

Clear as mud?

Last edited: May 23, 2005
5. May 23, 2005

### Cliff_J

Let me try to make it even easier to understand.

Ever heard static on a recording during a quiet passage? But when listening to the music its not quite as noticeable because its at so much lower a level? Right there you would have a signal and a level of noise, now its a matter of figuring out how much of each. And its easier to say 97db instead of saying the signal is 70,794 times bigger than the noise.

One thing to note about S/N ratios - its not always a very good indication of the quality of the equipment. It should be simple, but there is equipment (like Rane for example) that rates their S/N ratio with headroom on the signal and others who cheat how they achieve the number quoted. This discrepancy is so bad a piece with a 'lowly' 85db S/N ratio from a good source could be super quiet and a 107db 'awesome' piece has audible noise.

Another thing: A CD has a S/N ratio of 93db so exceeding this level is not necessarily useful.

6. May 24, 2005

### FredGarvin

I didn't know that about CD's. Ya learn something new everyday...

7. May 24, 2005

### nktvnvn

Thanks for all your help. What you say is really easy to undertand. Here is another question. Is the SNR a property of an audio device or is it kind of like a mechanism that improves the audio quality?

8. May 24, 2005

### FredGarvin

It is a property of the audio device. It is one measure of it's quality, hence the desire of some manufacturers to give false or misleading information regarding it.

9. May 24, 2005

### DaveC426913

Well, the signal-to-noise ratio is a number that gives a numerical indication of how well the signal is getting through, regardless of the reason. You can have mechanical devices creating noise (poor shielding on wires), natural phenomena (such as lightning) you can have interference (from powerful signals nearby) and all sorts of other things that will affect it, at various stages in its transmission/reception.

Any device (software/hardware, component, etc.) - such as Dolby noise reduction - that increases the signal-to-noise ratio is a good thing to have.

10. May 27, 2005

### Averagesupernova

Signal to noise ratio is not limited to audio devices.

11. May 27, 2005

### DaveC426913

While true, the question was specifically about audio. (In fact, I wandered from this myself, talking about SNR in EM transmissions such as radio.)

12. May 28, 2005

### FredGarvin

That is why my example was regarding a pressure transducer.

13. Jun 4, 2005

### nktvnvn

How do you get the number 70,794? Please show me. I know it has to do with logarithms.

14. Jun 4, 2005

### FredGarvin

In sound pressure measurements, the dB relationship used is

$$SPL = 20 Log \frac{P}{P_o}$$

Where:
$$SPL$$ = Sound Pressure Level in dB

$$P$$ = Measured pressure in $$Pa$$

$$P_o$$ = Reference pressure of $$20 \mu Pa$$

Last edited: Jun 4, 2005
15. Jun 14, 2005

### Cliff_J

And to followup on Fred's info, the antilog is really simple.

97 / 20 = 4.85

10^4.85 = 70,795 (ooops! I didn't round up!)

The decibel is like a decimeter, its prefix means its 1/10th the size of the unit following the deci part. A bel is a pretty big change and its easier to relate to it without having to use the decimals. Now why they didn't use this with the Richter scale to make that easier is another question, but regardless they are all still log scales used to describe things that would be far more difficult to understand on a linear scale.

http://www.hottconsultants.com/techtips/decibel.html

16. Jun 26, 2005

### Rogue Physicist

I have to comment here (having designed audio gear) that what appears to be 'cheating' is probably not in the simplistic sense of giving wrong numbers. Noise isn't the only way to degrade an audio signal. Manufacturers may fudge a little on various specs, but the S/N ratio isn't usually one of them, at least by much. (there may be some variation from unit to unit).

The usual differences you refer to in performance of audio gear has to do with other types of sound degradation. Distortion of the signal for instance isn't just an introduction of noise: One type of distortion is:

Harmonic Distortion. This type adds harmonics to the original signal (by distorting the wave shape) and amplifiers can have very low S/N ratios but high harmonic distortion, such as in a guitar amplifier. This distortion is often pleasing because the extra harmonics are musically related to the orignal signal, something like adding a choir to your soloist.

Intermodulation Distortion is another type, in this case usually very bad, because it muddies up the upper midrange and makes it difficult to hear the delicate tones of various instruments. As a result, stereo image is lost, and all the sounds are mixed together, and the vocals are hard to make out.

Flatness of Frequency Response This distortion is also common, and can be controlled by the user through tone controls. The frequency response is fixed to absolute frequencies, so that different songs (in different keys or vocal ranges) will sound different. Most systems suffer from this: critical bass is missing in the range from say 15 Hz to 30 Hz, large rooms have a low mid or bass 'ring' to them, and speaker systems with a crossovers (say around 1KHz-3KHz) drop out and distort parts of the musical scale where the tweeters and woofers overlap.

A music system is like a chain, only as strong as the weakest link, and often when the worst offending component is removed, another error, previously hidden becomes glaring and annoying.

This is why Signal to Noise Ratio is not the only or most important measurement of the quality of a system, and can be misleading if relied upon as a basis of selection.

You usually want high S/N ratio in a microphone, sensible harmonic distortion in a preamp, low intermodulation distortion in a power amp, and flat frequency response in a speaker system as a general guide.