When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Humans perceive sound by hearing. The human ear helps sound waves reach the brain, which then interprets the waves and creates the perception of hearing. The loudness of the environment in which a person is located determines whether they can distinguish between different sound sources.
The human ear can perceive an extensive range of sound intensity, necessitating the use of the logarithmic scale to define a physical quantity—the intensity level. It is a ratio of two intensities and hence a...

The loudness of a sound source is related to how energetically the source is vibrating, consequently making the molecules of the propagation medium vibrate. To measure the loudness of a source, the physical quantity of interest is the intensity. This is defined as the energy emitted per unit of time per unit of area perpendicular to the sound wave's propagation direction. Since the total energy is greater if the source vibrates for a longer duration and over a larger area, dividing the emitted...

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

When we hear a sound, our nervous system is detecting sound waves—pressure waves of mechanical energy traveling through a medium. The frequency of the wave is perceived as pitch, while the amplitude is perceived as loudness.