Final answer:
The minimum transition width Δ between the passband and stopband for a Medical DSP chip with a maximum FIR filter length of 129 and a sampling rate of 44.1kHz is approximately 342Hz.
Step-by-step explanation:
The subject of this question is related to signal processing in the context of Engineering, specifically the design of Finite Impulse Response (FIR) filters in Medical Digital Signal Processing (DSP) chips. When considering the design of such filters, one must specify the transition width, which is the frequency range between the passband and stopband, as well as the desired stopband attenuation.
In this scenario, the DSP chip can handle FIR filters with a maximum length of 129 taps at a sampling rate of 44.1 kHz. The minimum transition width Δ between the passband and stopband can be determined using the formula:
Δ = 2 × (1/length) × (rate/2) = (rate/length)
Where length is the maximum length of the FIR filter (129) and rate is the sampling rate (44.1kHz). Substituting these values into the formula, we get:
Δ = (44.1kHz/129) ≈ 342Hz
Therefore, the minimum transition width Δ is approximately 342Hz.