What method of analysis demonstrates that a signal such as a square wave is composed of a number of other signals added together
The correct answer and explanation is:
Answer:
The method of analysis that demonstrates a signal like a square wave is composed of a number of other signals added together is called Fourier Analysis, specifically the Fourier Series for periodic signals.
Explanation (300 words):
Fourier Analysis is a mathematical technique used to break down complex periodic signals into simpler components — specifically, sums of sine and cosine waves of different frequencies, amplitudes, and phases. When applied to a square wave, Fourier Analysis reveals that this waveform can be represented as the sum of multiple sine waves, each oscillating at a frequency that is an odd multiple of the fundamental frequency.
A square wave is a non-sinusoidal waveform that switches abruptly between two levels (e.g., +1 and -1). Although it looks very different from a smooth sine wave, mathematically it can be decomposed into an infinite series of sinusoidal waves. This infinite sum is known as the Fourier Series.
The Fourier Series for a square wave consists only of sine waves with odd harmonics — that is, sine waves at frequencies of 1×, 3×, 5×, 7×, etc., the fundamental frequency. Each harmonic has a specific amplitude that decreases as the harmonic number increases. When all these sine waves are added together, their constructive and destructive interference recreate the sharp edges and flat peaks characteristic of the square wave.
This decomposition is crucial in many fields such as signal processing, electronics, communications, and acoustics because it allows engineers to analyze, filter, or modify signals based on their frequency content. For instance, audio engineers can remove unwanted noise by filtering out certain frequencies, and electrical engineers can design circuits that respond to specific harmonics.
In summary, Fourier Analysis shows that complex periodic signals like square waves are not fundamental shapes on their own but rather combinations of simpler sinusoidal waves. This insight helps us understand and manipulate signals in both theory and practical applications.