Download An Introduction to Signal Detection and Estimation (Springer by H. Vincent Poor PDF

By H. Vincent Poor

Crucial history interpreting for engineers and scientists operating in such fields as communications, keep an eye on, sign, and snapshot processing, radar and sonar, radio astronomy, seismology, distant sensing, and instrumentation. The booklet can be utilized as a textbook for a unmarried direction, in addition to a mixture of an introductory and a sophisticated direction, or maybe for 2 separate classes, one in sign detection, the opposite in estimation.

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Extra info for An Introduction to Signal Detection and Estimation (Springer Texts in Electrical Engineering)

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Dramatic deviation from the ideal response shows that the normal Nyquist sampling rule is far too generous for applications requiring digital approximations to derivatives. Compared to the bilinear transform, the first difference operator has a superior magnitude response, but it is obtained at the expense of linear phase delay, which reaches 90° at U)=TT. In contrast, the bilinear transform has exactly the correct phase behavior over the whole Nyquist interval. ico = - I n Z . T h e difficulty arises because digital operators are formed from rational fractions of polynomials in Z , while ico is related to Z via the exponential function.

O n e of the chief properties of Z transforms is that their multiplication is equivalent to the convolution of their corresponding time sequences. , the same powers of Z ) . *JC 2 = (1,7,13,15) 29 Factoring Z Transforms into Couplets while the Z transforms of the two sequences are X {Z) = 1 + 5Z Y ^ ( Z ) = 1 + 2Z + 3 Z 2 2 giving for their product X (Z)X (Z) 1 = l + 7Z+ 2 13Z + 15Z 2 3 which is the Z transform of the convolution of x (t) with x (t). W e call this equivalence of convolution in the time domain with multiplication in the Z domain the convolution theorem.

A n y interpolation scheme must m a k e some assumption about the missing data. If we assume that the data behaves locally like a 3rd-degree polynomial, then the 4th difference o p e r a t o r should annihilate the data at every point. Use the 4th forward difference to find an o p e r a t o r that interpolates the center point from its four neighboring points, two on each side. Give an example of an unstable sequence. Give an example of a stable causal sequence. W e would like to m a k e a digital recording of a 3-minute-long stereo music performance.

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