DSP in Hearing Aids

Read pages 4-6.

With a partner go over Example 1. "A hearing aid."

1. Write down all the key terms DSP terms that you encounter and write a definition for them.

Key Terms:

• A/D Converter - Used to transform the analog input signal into a digital signal via acquiring samples from the signal at (normally equal speed time intervals and converting the level of these samples into a numeric representation that can be interpreted by a digital signal processing system. Requires low-pass filter prior to analog to digital (A/D) conversion

• Digital Signal Processing (DSPS) - A process which performs arithmetic operations on the input sequence. Typically, the desired signal inputs are enhanced in the output signal while noise and artifacts are suppressed.

• D/A Converter - Used to convert the DSPS output into analog samples that are equally spaced in time.

• Lowpass Filter - Used to convert the analog samples into a continuous-time signal; moreover, this step is equivalent to an interpolation operation between the discrete analogue samples produced in the D/A converter.

2. Draw a block diagram all of the steps in the DSP chain going from input to output. (Figure 1 can be a useful guide).

See images below

3. Explain why harmonics are discussed, in what context, and how are the expressed.

Harmonics are discussed in this DSP hearing aid flash lab because in signal analysis, periodic signals serve as basic signals from which many other signals can be constructed and analyzed. The sinusoid sin(wt) is a periodic signal since, sin(w + 2pi)t = sin(wt). Periodic signals can be harmonically related this means that they consist of a set of periodic signals whose fundamental frequencies are all multiples of a single positive frequency (w). Moreover, the periodic signals sinusoid sink(wt), for any integer k, is called the k-th harmonic of sin(wt). In signal analysis, a linear transformation of the signal from the time domain to the frequency domain and vice versa, depending on the domain in which either the relevant information is exposed in a clearer way or the mathematical manipulations are simpler. In the case of periodic signals, they have quite compact representation in the frequency domain where only the fundamental frequency information (w) and their harmonics are required, whereas in the time domain they are represented by a continuous function of time. Overall, this information is useful when applied to hearing aids harmonics will allow for them to focus on certain frequencies of sound meaning the user can have selective hearing and focused hearing in the direction which the sound is being projected. This allows the user to cancel out other unwanted noises and frequencies which will distort the clear and actual signal which the user desires to hear meaning focused sound.

4. Which of the concepts learned in the course so far seem applicable and how?

The concepts learned in this course which are applicable include sampling, sampling frequency, and Nyquist rate. Moreover, it is important when sampling to determine what the maximum frequency of the signal is or the one which is desired to ensure that no noise is present. Using an anti-alias or lowpass filter prior to A/D conversion will allow for the signals at or below the maximum frequency to be cut off from the signal which will prevent aliasing. Additionally, once the maximum frequency is known and the lowpass filter is used, the sampling frequency will need to be equal to 2 times the maximum frequency of the signal which will lead to the identification of the Nyquist rate. This is important to consider such that the signal is not broken during A/D conversion and is able to be fully restored during D/A conversion to produce the correct continuous signal present prior to sampling.