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<h2>Hello! It will be a pleasure to help you! </h2><h2>So let's get started:</h2><h3 /><h2>PART 1. </h2><h3>An analogue sensor signal is sampled every 0.4ms to convert it into a digital representation. What is the corresponding sampling rate?</h3>
Sampling is simply a reduction of a continuous time signal to a discrete time signal. Here we know that an analogue sensor is sampled every to convert it into a digital representation. So sampling rate, also called the sampling frequency or
, is the average number of samples obtained in one second, that is, samples per second:
Since we know:
Then, the sampling rate is:
Sampling Theorem (Nyquist Theorem) States:
<em>A </em><em>continuous time signal </em><em>can be completely represented in its samples and recovered back, if the sampling frequency </em> <em>is greater than or equal to twice frequency component of the message signal.</em>
In other words:
So, the highest frequency in the digital representation will be:
Everything is Ok up to this point! But let me explain something. We do all these things in order to get a faithful reproduction of the digital signal. So the Analog-to-Digital Conversion (ADC) allows us to do that.
In this final part, each sample is quantised to 2048 levels, so this number can be written as:
That is, there are , in other words, it takes:
Finally, the resulting bit-rate is:
In scientific notation to two decimal places: