Use of this web site signifies your agreement to the terms and conditions. Two methods for the reduction of quantization effects in recursive digital filters Abstract: Two distinct methods for the reduction of coefficient and product quantization effects in recursive digital filters are described. A degree of freedom is introduced in the design by increasing the approximation order above the minimum.
This is then used to increase the allowable margin for coefficient quantization error or to reduce the sensitivity to coefficient quantization. The two methods are used to design several sixth-order low-pass filters. The designs obtained are then compared with the corresponding minimum-order elliptic designs with respect to the effects of coefficient and product quantization. DSP practitioners can use two tricks to reduce converter quantization noise.
Thoseschemesare called oversampling and dithering. We merely sample an analog signal at an fs sample ratehigher than the minimum rate needed to satisfy the Nyquist criterion twice theanalogsignal's bandwidth , and then lowpass filter. What could be simpler? The next assumption is: the quantization noise values are trulyrandom, and in the frequency domain the quantization noise has a flatspectrum. Thus we can consider the idea that quantization noise can berepresented as a certain amount of power watts, if we wish per unitbandwidth.
The amplitude of this quantization noise PSD is the rectangle area total quantization noise power divided by the rectangle width f s , or. That would make the lsb valuesmaller and certainly reduce PSDnoise, but that's an expensivesolution. Extra converter bits cost money. Better yet, let's increasethe denominator of Eq. Next we lowpass filter the converter's output samples. At theoutput of the filter, the quantization noise level contaminating oursignal will be reduced from that at the input of the filter.
The improvement in signal to quantization noise ratio, measured indB, achieved by oversampling is:. Thusoversampling by a factor of 4 and filtering , we gain a single bit'sworth of quantization noise reduction. After digital filtering, we can decimate to the lower fs,old withoutdegrading the improved SNR.
With the use of a digital lowpass filter, depending on theinterfering analog noise in x t , it's possible to use a lowerperformance simpler analog anti-aliasing filter relative to theanalog filter necessary at the lower sampling rate. This scheme, which doesn't seem at all like a good idea, can indeedbe useful and is easily illustrated with an example.
The x1 n output sequence is clipped. This generates all sorts ofspectral harmonics. Because the quantization noise is highly correlated with our inputsinewave — the quantization noise has the same time period as the inputsinewave — spectral averaging will also raise the noise harmoniclevels.
Dithering to the rescue. Dithering is the technique where random analog noise is added to theanalog input sinusoid before it is digitized. Dithering raises the average spectral noise floor but increases oursignal to noise ratio SNR2. Dithering forces the quantization noise tolose its coherence with the original input signal, and we could thenperform signal averaging if desired.
For high-performance audio applications, engineers have found thatadding dither noise from two separate noise generators improvesbackground audio low-level noise suppression. Because the convolution of two rectangular functions is triangular,this dual-noise-source dithering scheme is called triangular dither.
Typical triangular dither noise has rms levels equivalent to, roughly,2 lsb voltage levels. In the situation where our signal of interest occupies some welldefined portion of the full frequency band, injecting narrowband dithernoise having an rms level equivalent to 4 to 6 lsb voltage levels,whose spectral energy is outside that signal band, would beadvantageous. Remember though: the dithersignal can't be too narrowband, like a sinewave. Quantization noisefrom a sinewave signal would generate more spurious harmonics!
That narrowband dither noise can then be removed by follow-ondigital filtering. This way, we randomized the quantization noise, but reduced theamount of total noise power injected in the analog signal. This schemeis used in commercial analog test equipment. Thebook can be purchased on line. Richard Lyons is a consultingsystems engineer and lecturer with Besser Associates. You must Sign in or Register to post a comment. This site uses Akismet to reduce spam.
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