Abstract
The previous chapter introduced the concept of a random process and explored in depth the temporal (i.e., time-related) properties of such processes. Many of the specific random processes introduced in Chap. 7 are used in modern engineering to model noise or other unpredictable phenomena in signal communications. In this chapter, we investigate the frequency-related properties of random processes, with a particular emphasis on power and filtering.
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Notes
- 1.
Readers already familiar with filters will recognize the terms “lowpass” and “bandpass.” We will see these terms again in the next section.
- 2.
Readers interested in a thorough treatment of filters and other systems should consult the reference by Ambardar.
- 3.
Please note: The case of a deterministic signal x(t) must be handled somewhat differently. Consult the reference by Ambardar for details.
- 4.
In this context, the Kronecker delta function is also commonly called the unit sample response, since it is strictly speaking not an impulse (its value is well defined at zero). It does, however, share the two key properties of a traditional Dirac delta function (i.e., an impulse): it equals zero for all non-zero inputs, and the sum across its entire domain equals 1.
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Carlton, M.A., Devore, J.L. (2017). Introduction to Signal Processing. In: Probability with Applications in Engineering, Science, and Technology. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-52401-6_8
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DOI: https://doi.org/10.1007/978-3-319-52401-6_8
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