The purpose of Digital Signal Processing $($DSP$)$ is to manipulate and analyze digital signals to extract useful information or enhance their quality for various applications. DSP encompasses a wide range of techniques and algorithms that operate on digital signals, which are discrete$-$time sequences of sampled data.

Digital Signal Processing $($DSP$)$ can be implemented on Arduino Uno to perform various tasks such as filtering, modulation, and signal analysis. Below is a simple example demonstrating how to generate a sine wave using Direct Digital Synthesis $($DDS$)$ technique, which is a common application of DSP on microcontrollers like Arduino Uno:

The code example provided generates a sine wave on pin $9$ using DDS technique. The sine wave is synthesized using a precomputed lookup table of sine values. The frequency of the generated sine wave can be adjusted by changing the value of FREQ. Keep in mind that the maximum frequency may be limited by the processing power of the Arduino Uno and the speed of the DAC $($Digital to Analog Converter$).$

$//$ Arduino Uno DDS Sine Wave Generator

#include

const uint$16\_$t SINE$\_$TABLE$[]$ PROGMEM $=\{$

$2048,2098,2148,2197,2246,2294,2341,2387,2432,2476,2519,2560,$

$2599,2637,2673,2707,2739,2770,2798,2825,2849,2872,2892,2911,$

$2927,2941,2953,2963,2970,2975,2977,2977,2975,2970,2963,2953,$

$2941,2927,2911,2892,2872,2849,2825,2798,2770,2739,2707,2673,$

$2637,2599,2560,2519,2476,2432,2387,2341,2294,2246,2197,2148,$

$2098,2048,1998,1948,1899,1850,1802,1755,1711,1668,1624,1581,$

$1540,1501,1463,1427,1393,1361,1330,1302,1275,1251,1228,1208,$

$1189,1175,1161,1151,1143,1138,1136,1136,1138,1143,1151,1161,$

$1175,1189,1208,1228,1251,1275,1302,1330,1361,1393,1427,1463,$

$1501,1540,1581,1624,1668,1711,1755,1802,1850,1899,1948,1998$

$\}$;

const uint$8\_$t TABLE$\_$SIZE $=$ sizeof$($SINE$\_$TABLE$)/$ sizeof$($SINE$\_$TABLE$[0])$;

const int WAVE$\_$OUTPUT$\_$PIN $=9$;

const float SAMPLING$\_$FREQ $=10000\mathrm{.}0$; $//$ Hz

const float FREQ $=1000\mathrm{.}0$; $//$ Hz

const float PHASE$\_$INCREMENT $=($FREQ $/$ SAMPLING$\_$FREQ$)*$ TABLE$\_$SIZE;

uint$16\_$t phaseAccumulator $=0$;

void setup$()\{$

pinMode$($WAVE$\_$OUTPUT$\_$PIN, OUTPUT$)$;

$\}$

void loop$()\{$

$//$ Calculate next sample

uint$16\_$t sample $=$ pgm$\_$read$\_$word$\_$near$($SINE$\_$TABLE $+($phaseAccumulator $>>8))$;

$//$ Output sample to DAC

analogWrite$($WAVE$\_$OUTPUT$\_$PIN, sample $>>4)$;

$//$ Update phase accumulator

phaseAccumulator $+=$ PHASE$\_$INCREMENT;

$//$ Wrap phase accumulator

if $($phaseAccumulator $>=($TABLE$\_$SIZE $<<8))\{$

phaseAccumulator $-=($TABLE$\_$SIZE $<<8)$;

$\}$Questions:

Code Questions:

$1.$ How does the provided Arduino code utilize Direct Digital Synthesis $($DDS$)$ to generate a sine wave, and what are the key components involved in this process?

$2.$ Explain the significance of the $`$SINE$\_$TABLE$`$ array in the context of the code, and how does it contribute to the generation of the sine wave?

$3.$ What role does the $`$PHASE$\_$INCREMENT$`$ variable play in the code, and how is it calculated based on the desired frequency and sampling frequency?

$4.$ Describe the operation performed in the $`$loop$()`$ function and how it ensures the generation of a continuous sine wave.

$5.$ Discuss the purpose of the $`$phaseAccumulator$`$ variable in the code, including how it is updated and why it is necessary for generating the sine wave.

DSP Questions:

$1.$ Define Digital Signal Processing $($DSP$)$ and explain its significance in modern technology.

$2.$ Discuss the differences between analog signal processing and digital signal processing, highlighting the advantages of DSP$.$

$3.$ Explain the fundamental principles of sampling and quantization in the context of digital signal processing.

$4.$ Describe common applications of DSP across various domains such as telecommunications, audio processing, image processing, and biomedical signal processing.

$5.$ Discuss the challenges and limitations associated with implementing DSP algorithms in real$-$time systems and embedded devices, and propose strategies for overcoming them.