Why do digital signals have an infinite bandwidth
Why do all digital signals have an infinite bandwidth?
Constructing a discontinuous voltage waveform as the sum of sine waves would require an infinite number of sine waves. A "perfect" digital signal immediately switches between VSS and VDD (or vice versa). Such instantaneous switching events would represent discontinuities in the waveform.
In practice, chips neither generate perfect digital signals at their outputs, nor do they need them at their inputs. Examining an output signal in a sufficiently good range will usually show that it is a little "smoothed", and most chips will tolerate input signals that are essentially "smoothed" provided they don't linger or hop around in the 1/4 range and 3/4 VDD. In fact, some chips are designed to intentionally smooth their output waveforms (sometimes by a programmable amount) and / or accept inputs that are even "muddy" smoothed to a point.
It's worth noting that while something like a perfect 1 Hz square wave can be expressed as the sum of continuous sine waves in the 1 Hz to 1 MHz range and beyond, it is very unlikely that a device capable of receiving of a 1 MHz signal, a 1 Hz rectangle perceives a wave with a continuous 1 MHz component. The 1 Hz square wave would contain, among other things, a 999,999 Hz component whose strength was 1 / 999,999 of the fundamental wave and a 1,000,001 Hz component whose strength was 1 / 1,000,001 of the fundamental wave. The device trying to receive a "1 MHz" signal would detect these and many other components to varying degrees; During each one second interval there were times when they were all in phase and times when about half were in phase and half out. The device would thus sense a variable amount of "1 MHz" signal - most likely sense a considerable amount near the moments when the input switched (because all the waves sensed would be in phase) and a much smaller amount at other times ( because the detected waves would have a mixture of phases). A really sharp 1 Hz square wave driving a strong antenna would therefore not cause continuous interference in a 1 MHz transmission, but would result in a 2 Hz "tick-tick-tick".
- How do I escape a diagnosis of schizophrenia
- Contains plastic carbon
- What is a wireless RF keyboard
- Mercury has floating properties
- Is Jimmy Wales proud and arrogant himself
- The desire to be obese is widespread
- How does China's nationalism help it thrive?
- Can you get phones on an airplane
- Feel responsible to humanity
- Do you think hardship is character building
- Is Duke 200 for short riders
- What is Chapter 7 Bankruptcy 1
- What all websites expose Narendra Modi to
- Why is Nginx better than apache server
- What does Kanishk
- Why are conservative values no longer popular?
- How much can a piranha eat
- Have laptop batteries ever caught fire?
- How is technology used in business administration
- The commercial sale of water should be banned
- Why is coaching important to JEE
- Why do crusts itch and become crispy
- I can learn
- Why shouldn't kids watch porn
- How can I get a bonus every day
- What is your opinion on Wealthsimple
- How to learn Zhuyin Fuhao
- Wouldn't you marry a raped girl
- How do you feel about heterosexuality
- Which is the most reliable bitcoin platform
- Where do you get a heavenly feeling from
- What's the fastest topic on Tumblr
- Who created Isockets two minute product video
- What is the website cameo