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what is noise shaping?

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Full Member level 1
Oct 15, 2007
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first order noise shaping

please help me understand the concept of noise shaping :D

1- What is noise shaping?
2- What is first-order noise shaping?
3- What is the difference between first-order noise shaping and second-order or third-order ... noise shaping?
4- Can anyone describe noise shaping in time domain?

Thank you

1. When you quantize a signal, you're basically rounding the signal to the nearest value you have a representation for (eg. for an 4-bit ADC operating between 0V and 1V, you can represent the values 0:1/((2^4) - 1))):1, where (1/((2^4)-1) is an LSB. The act of rounding a signal value, say 0.214 to the nearest value you can represent, 0.2, introduces an error (of 0.014 in this case). If you have 1000 different signal values which you quantize, then in probability terms, the error will be uniformly distributed between +/- 0.5*LSB.

In the frequency domain, these errors look like noise which is uniformly distributed across the spectrum. For a 4-bit ADC, in the output spectrum you would see your signal and also some noise somewhere around 24dB down (4-bit @ 6dB/bit). Noise shaping involves shaping this noise so that less of it appears at low frequency (where your signal is) and more of it appears at high frequency, so that for example, your noise floor will be -80dB in the signal band, but -10dB at high frequency. But that's not a big deal as you can use a low-pass filter at the output of your ADC with a cutoff higher than the highest signal frequency, but below the point at which the noise starts getting too high, to bring the high frequency noise down also to -80dB. So in this example, noise shaping has achieved 13-bit performance from a 4-bit ADC.

Have a look at this intersil application note: **broken link removed**, especially figure 7C.

2. Noise shaping uses a high pass filter to attenuate noise in the signal band, and to move it to high frequency. First order noise shaping uses a first order high pass filter.

3. Second/Third/n order noise shaping uses a Second/Third/n'th order high pass filter.

4. No.
what is noise?

It's not something that can be explained in a few sentences easily. If you do some reading about sigma-delta ADCs you will see noise shaping explained. But like ansu_s said, noise shaping moves some of the quantization noise to higher frequencies. In an oversampling converter, much of this noise can be pushed above the signal bandwidth and the anti-alias filter can eliminate that portion of the quantization noise.

The orders of noise shaping refers to the complexity of the feedback stage in the delta-sigma converter. Higher orders can shape the noise better. But this feedback then introduces a phenomenon called "tones" that need to be eliminated.
noise shaping

Dear ansu_s and snafflekid, thank you for your replies.
I've read the application note and finally I could understand and convinced myself that sigma-delta modulation and the fundamental equation of
can reduce inband noise, compared with the simple sampling method, eq.5


But I can't understand how noise shaping moves the noise to higher frequencies!?

Maybe you can help me by answering the question below:

How does Eq.8 results from Eq.7 ?


I think I must integrate square of Eq.7 between 0 and f0, but the result is not equal to Eq.8 :!: :?:

what is noise

the faster the freq. the more average action performed at the input node, the more accurate it is.

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