Chapter 1Introduction

U. Zölzer

In this first chapter, we will introduce the basics of signals and systems, and describe the transmission of signals through these systems [Opp14]. These fundamental concepts and the describing algorithms lay the foundation for digital audio signal processing. We will start with analog signals and analog systems, then we will sample the analog signals and perform digital signal processing, and finally reconstruct an analog output signal from the digital output signal. Figure 1.1 shows a typical audio application of capturing a vocalist and transmission to a loudspeaker via an amplifier for reproduction in another room for a listener or listening audience. The microphone delivers an electrical input signal x left-parenthesis t right-parenthesis and the output signal y left-parenthesis t right-parenthesis is the signal that will be received by the listener's ear. Both signals are continuous‐time input and output signals. The entire chain of operations from microphone, amplifier, loudspeaker, and sound transmission through the listening room to the listener can be modeled by a system with a continuous‐time impulse response h left-parenthesis t right-parenthesis. Such an impulse response can be acquired by an impulse response measurement approach. The entire continuous‐time ...

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