Basic DSP Theory
Will C. Pirkle · 2019
In order to intuitively understand the foundation of digital signal processing (DSP) theory, the reader need to review some math and engineering concepts. Mathematically, two functions are orthogonal if their inner product is zero. When this happens, the two functions are maximally dissimilar. This means that mathematically speaking, sin and cos are as dissimilar as night and day, hot and cold, etc. The next piece of DSP theory the reader want to understand is the concept of time delay as a mathematical operator. Mathematically, time can run backwards. The transfer function is complex because it contains complex numbers; many transfer functions are actually quite simple. For each evaluation frequency, the magnitude of the transfer function is the product of the inverse lengths of the two vectors to each pole-pair. The biquadratic transfer function has a numerator polynomial with a maximum polynomial exponent of two, and so does the denominator.