Quantization Error Sound Like
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How To Reduce Quantization Error
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Types Of Quantization
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What Is Quantization
takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How does the quantization error generate noise? up vote 9 down vote http://www.sweetwater.com/insync/quantization-error/ favorite 3 I'm learning about sampling and DSP on my own. I have a hard time to understand how the quantization error results in noise. I think I miss a fundamental understanding but can't tell what it is. So how does the quantization error generate noise? noise sampling share|improve this question asked Jul 15 '12 at 19:29 Jan Deinhard 1485 It's more distortion than noise. It depends on the signal, and is not random. –endolith Jul 15 '12 at 20:48 http://dsp.stackexchange.com/questions/2897/how-does-the-quantization-error-generate-noise endolith, I think what I don't understand is how the error results in frequencies. –Jan Deinhard Jul 15 '12 at 21:04 2 distortion always produces additional frequencies. if you distort a sine wave, it becomes a different repetitive waveform. any repetitive waveform other than a sine wave is made up of multiple frequencies. –endolith Jul 15 '12 at 22:58 1 As @endolith has mentioned, let us assume you have a very bad ADC, such that you give it a pure tone, but get a signal that looks like a sine but has big steps in it. (So now your signal looks like a staircase that is going up and down with the original sine.) Now, you know intuitively that a step is composed of many frequencies. This is how an ADC will add frequencies as you are asking. It is a non-linear operation btw. If it was linear, you could not make new frequencies, only superimpose many of them together. –Mohammad Jul 16 '12 at 14:33 add a comment| 3 Answers 3 active oldest votes up vote 6 down vote accepted Suppose I have a multitone signal (six carriers, at ±1/1000, ±2/1000 and ±7/1000 of sampling frequency) x = (1:1000); wave = sin(x/1000*2*pi) + sin(x/1000*2*pi*2) + sin(x/1000*2*pi*7); which is quantized using a 14-bit ADC wave_quant = round(wave * 16384) / 16384; The difference wave_qnoise = wave_quant - wave; gives the quantization error The corresponding spectrum wave_qnoise_freq = mag(fftshift(fft
However, the CD standard remains at 16-bit/44.1kHz. Somehow, the DAW user has to get the 24-bit file into a 16-bit file. So what are the options available to the DAW user? Bit Resolution: Bit resolution http://www.pcrecording.com/dither.htm refers to the number of bits a soundcard can use to express the amplitude of an audio sample. Each bit can resolve 6dB of amplitude information - - the addition of each bit results in 6dB more amplitude range. The total number of bits available is referred to as bit depth. The total of the amplitude information is known as dynamic range. Dynamic range: Dynamic range is the difference between the quietest quantization error and the loudest amplitude a soundcard can record. Dynamic range is determined by the number bits the soundcard can use to resolve the amplitude of the signal. As bit depth increases so does the dynamic range. This means the threshold for the quietest signal that can be recorded goes down and the threshold for the loudest signal that can be recorded goes up. A 16-bit signal has a 96dB dynamic range. A quantization error in 20-bit signal dynamic range is 120dB. A 24-bit signal dynamic range is 144dB. What does this have to do with noise? All analog systems have inherent system noise. Digital systems have no system noise but do introduce quantization errors which sound like noise. So, in terms of digital noise, each additional bit reduces the audible level of quantization error by 6dB. Quantization error: Each bit represents a quantization interval - - with a discrete threshold for its amplitude range. In an analog waveform, there is an equivalent dynamic range that exists between each digital 0 and 1. When the analog signal amplitude being sampled falls between a quantization interval (each bit), the system cannot resolve the analog amplitude of the input signal and simply truncates it. The result is a square wave for each instance where the digital device cannot reconcile the difference. These square waves leave digital artifacts that do not represent any frequency in the analog waveform. This is known as quantization error. The amplitude of an analog waveform can be graphically represented by a continuous smooth curve. As one moves through/across the waveform over time, the amplitude seamlessly changes. In digital recording however, the soundcard can only record discrete "levels" of amplitude. There is a distinct plateau to each level. Th