The Mathematics of Signal Processing | The z-transform, discrete signals, and more

The Mathematics of Signal Processing | The z-transform, discrete signals, and more

Sign up with Dashlane and get 10% off your subscription:

STEMerch Store:
This video goes through an overview of what you would learn in a discrete time signals (or digital signal processing) course. Sampling, digital filters, the z-transform, and the applications of these are some of the things included. I had to over simplify a lot to barely keep this video under 30 minutes but hopefully it gives you an idea of how this type of math is used in the real world.

Pole/Zero plot and digital filter modeler used in video:

Join Facebook Group:

Support the Channel:
PayPal(one time donation):

Animations: Brainup Studios (email:

β–ΊMy Setup:
Space Pictures:
Magnetic Floating Globe:
Equilibrium Tube:

β–ΊCheck out the MajorPrep Amazon Store:


  1. Pankaj Chauhan on May 4, 2022 at 9:11 pm

    Its just so amazing.

  2. Karan Kakkar on May 4, 2022 at 9:13 pm

    Can you please talk about more engineering topics and their applications. Ik you already did integral transforms, complex numbers, egienvalues/vectors etc but there are so many more cool topics to cover.

  3. Aaron Barber on May 4, 2022 at 9:16 pm

    This is the class i just took in a nutshell!

  4. g7sky on May 4, 2022 at 9:18 pm

    u on drugs lol amazing

  5. Chac Mool on May 4, 2022 at 9:20 pm

    Can anyone suggest an online course on this with coding (in R or Python) as an integral part of the course? I am an old EE who needs a big refresher.

  6. Arun Kumar P.V on May 4, 2022 at 9:20 pm

    What software are you using for the real-time frequency response plot from the z-plane pole-zero plot ?

  7. Lundo on May 4, 2022 at 9:22 pm

    Computer Engineering student here. Taking Signals and Systems this fall.

  8. Anguraja Renganathan on May 4, 2022 at 9:22 pm

    I love watching your video , Greetings from Tamilnadu, India

  9. Francesco Moltisanti on May 4, 2022 at 9:23 pm

    Hi, I’m a student with disabilities and learning difficulties. Looking to hire someone to help me through this for the Spring semester. Covered topics: Python 3, programming, Sampling and Quantization, Signal Processing, The Fourier Transform, LTI Systems, and Convolution, Non-Linear systems

  10. Justin Cao on May 4, 2022 at 9:25 pm

    Im taking DSP class rn, this video is really helpful with visualization. Very well constructed and easy to follow. Please keep up your work! Thank you

  11. Sairampavan T on May 4, 2022 at 9:26 pm

    Why youtube kept recommending this video to me from three days..continuously..🀨

  12. mukul jobra on May 4, 2022 at 9:27 pm

    It was really wonderful looking throughout the whole video, in every minute, you just simplified very in-depth topics, especially about what power the DSP is actually holding in the digital era. Make some more videos on similar stuffs like Laplace and Fourier transforms, the world must need to know what actually these two geniuses have given to us.
    Great πŸ‘πŸ»πŸ‘πŸ»πŸ‘πŸ»πŸ‘πŸ»

  13. Wicked Stereo on May 4, 2022 at 9:29 pm

    *watched one of your videos..


  14. Kari Hotakainen on May 4, 2022 at 9:31 pm

    Not distance, but difference. Distance is a non negative quantity.

  15. Muhammad Nada on May 4, 2022 at 9:31 pm

    It’s not obvious how the poles and zeroes are placed according to the required frequency on 23:15

  16. Anish Sharma on May 4, 2022 at 9:32 pm

    god , this is a gift to humanity such amazing explainations , i can only stand in awe

  17. g7sky on May 4, 2022 at 9:32 pm


  18. yorch877 on May 4, 2022 at 9:32 pm

    Your videos are really great, even for us graduates. Thank you!

  19. A B on May 4, 2022 at 9:37 pm

    This cleared the whole connection between z-transform and poles/zeros, and the link between circle and sinusoid. Much appreciated.

  20. alex Lo on May 4, 2022 at 9:38 pm

    I almost threw my DSP 90’era textbook into bin when I see this clip.
    By the way ,why don’t add detail on real frequency because the clip did on normalized throughout the time. Such there are any constraint in freq sampling.

  21. Laois Hinsen on May 4, 2022 at 9:41 pm

    nope, that was not smooth at all
    i don’t get it yet, but i will leave the like for the effort

  22. Laois Hinsen on May 4, 2022 at 9:41 pm

    i am a computer engineering student and we take both continues and digital, each in separate course
    what i understood from this video is that Digital signal processing have mathematical function that acts as low/high/band filter without needing a physical filter to be changed which is amazing

  23. balaji sriram on May 4, 2022 at 9:44 pm

    man you are a genius!!!

  24. Chuckyae on May 4, 2022 at 9:45 pm

    Aint -1+1= 0 !!! guys i got drunk here !

  25. Philippe Zevenberg on May 4, 2022 at 9:46 pm

    Me: "thinks of Fourier for some reason"
    Zach: "speaks about Fourier"
    Me: "Am… am I learning? o_o"

  26. Card & Code on May 4, 2022 at 9:47 pm

    What kind of physics beside classical mechanics is used in controls engineering ?
    What beside electronics, should I learn in it ?

  27. raphaelkuttruf on May 4, 2022 at 9:47 pm

    22:45 Nope, the filter didn’t introduce that much distortion.
    The distortion came because you mixed your vocal with that 1kHz sine wave "way too hot".
    Then the mixed signal was forced to clip/distort at the 0dB ceiling when rendering. Look at your meter going into the dark red area.
    Distortion adds even and odd overtones, which you can’t easily filter.
    There is no easy way to go back to your clean vocal, even though you removed that 1kHz successfully.
    Greetings by a triggered Audio Engineer xDD

  28. Jie Zhang on May 4, 2022 at 9:48 pm

    Fantastic vedio!

  29. moh on May 4, 2022 at 9:49 pm

    Engineering = Applied Mathematics = Advanced Math
    signal and system, digital signal processing, electromagnetic, control systems
    are some of the hardest engineering subjects
    coz they demand a lot of advanced math

  30. Jacob Penn on May 4, 2022 at 9:49 pm

    Wow this finally makes sense

  31. Nono Jackk on May 4, 2022 at 9:50 pm

    How does this guy explains a whole semester-long course in a single video better than my professors did in 15 hours!?

  32. gaetano di giorgio on May 4, 2022 at 9:51 pm

    Soft music and analysis
    The top for a sucker!

  33. Buh on May 4, 2022 at 9:53 pm

    I had never heard of signal processing, and after the first watch, I understand some parts; you did an excellent job here. Thanks, Zach.

  34. Antoinette Amal on May 4, 2022 at 9:53 pm

    Awesome should team up with AhmadBazzi πŸ™ŒπŸ»

  35. Kimiru on May 4, 2022 at 9:55 pm

    Wait, at 9:00, shouldn’t pi/3 be smaller than pi/2….?

  36. Thalles Antonio Souto on May 4, 2022 at 9:55 pm

    puta que pariu! Que obra de arte esse video…

  37. A C on May 4, 2022 at 9:55 pm

    I have an ABET electrical engineering degree. This the kind of video I want to make but I never get around to because 40 hours for 40 expected viewers just isn’t worth my time. Seeing over 200k views puts me in shock and awe!

  38. scarlet 001 on May 4, 2022 at 9:57 pm

    interesting can u produce more other genius guys who never want to share knowledge secrets stuff

  39. Jayjay McFly on May 4, 2022 at 9:58 pm

    In the future: Zach and 3B1B team up and hijack the whole education system.

  40. Fraz Ajmal on May 4, 2022 at 9:58 pm

    Dude. Honestly. Really good video. Please keep making these.

  41. Ander Santos on May 4, 2022 at 9:59 pm

    ok so where are the fourier series?

  42. Attila on May 4, 2022 at 9:59 pm

    This was what is going on behind the maths of ee. I am so grateful

  43. Juan carlos crovett on May 4, 2022 at 9:59 pm

    it was pretty good

  44. Ahmed Minai on May 4, 2022 at 10:00 pm

    I watched this video when it first came out. Didn’t realize it would be this useful in my junior year of college where we’re studying signal processing.

  45. Frank DiMeglio on May 4, 2022 at 10:02 pm


    TIME is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity ON BALANCE. Gravity IS ELECTROMAGNETISM/energy. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. ("Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity.) E=MC2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. E=mC2 IS F=ma. SO, the middle distance in/of/AS SPACE AND the full distance in/of/AS SPACE are NECESSARILY linked AND balanced; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (The stars AND PLANETS are POINTS in the night sky. The sky is blue, AND THE EARTH is ALSO BLUE.) THE EARTH/ground AND THE SUN CLEARLY reveal that E=MC2 IS F=ma ON BALANCE. It all CLEARLY makes perfect sense. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. BALANCE AND completeness go hand in hand. The ultimate mathematical unification of physics/physical experience combines, BALANCES, AND INCLUDES opposites, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY ON BALANCE !! TIME dilation ULTIMATELY proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, AS E=MC2 IS F=MA ON BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS E=MC2 IS F=MA ! Gravity IS ELECTROMAGNETISM/energy. It ALL CLEARLY makes perfect sense !

    By Frank DiMeglio

  46. Sami Siddiqi on May 4, 2022 at 10:03 pm

    Not thirty seconds in and you’re already swearing 0:12 🀬

  47. BusterofGlitch on May 4, 2022 at 10:04 pm

    I study electrical engineering. I have an exam on this topic tomorrow lol. Thanks for the video, you are explaining it better than the lectures! πŸ™‚

  48. Phone Zaw Thein on May 4, 2022 at 10:06 pm

    thank u very much for this video.

  49. Mark Watson on May 4, 2022 at 10:09 pm

    Great video.

  50. R N on May 4, 2022 at 10:10 pm

    This is what I did with edm music, where I would take a single clip and do the zoom in for pure sine and bumping little chops of sound, that if taken from the entire clip, then in my minimum music knowledge…it remains in tune?