uniform-quantizers

# uniform-quantizers - EE380 Communication Systems Spring...

This preview shows pages 1–2. Sign up to view the full content.

EE380: Communication Systems Spring 2010-2011 Quantization Error and Quantization Noise (For a Uniform Quantizer) Consider a quantizer whose input signal is x ( t ) and the output is the quantized signal y ( t ). Then the quantization error q ( t ) = y ( t ) - x ( t ). For a given sample, we define: q = Y - X . When the probability density function of X is smooth and the number of quantization intervals ( L ) is large, we will find an expression for quantization noise, i.e., power of q ( t ) without assuming that q is a uniform random variable. Let the density function of X is f X ( x ). We define p k as the probability that X lies between x k - 1 and x k (see figure). Note that x k - 1 and x k are the end points of the k -th quantization interval. Whenever X falls within this interval, the output of the quantizer is y k . The corresponding quanti- zation error is y k - X . Clearly, the proba- bility of this error occurring is p k . Δ p (x) X X x x k-1 k k p Thus, the quantization noise (power of the quantization error signal) is given by: N q = L summationdisplay k =1 x k

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern