What is Digital Signal?
Summary
TLDRThis lecture distinguishes between analog, discrete time, and digital signals. It explains that digital signals discretize both time and magnitude, unlike discrete time signals which only discretize time. The lecture uses temperature and voltage examples to illustrate how digital signals can only take certain fixed levels, leading to quantization errors that can be minimized by increasing the number of levels. The need for digital signals will be discussed in the next lecture.
Takeaways
- 🕒 The lecture focuses on the concept of digital signals, which are different from analog and discrete time signals.
- 📊 Digital signals require discretization of both time and magnitude, unlike discrete time signals which only discretize time.
- ⏱️ Time discretization is achieved by dividing the time axis into equal intervals, calculated using the formula delta T = (Tn - Tn-1).
- 📉 Magnitude discretization involves dividing the magnitude axis into fixed levels, allowing the signal to take only specific values.
- 🌡️ An example is given where temperature is measured at discrete time intervals, and then the magnitude is also discretized for a digital signal.
- 📉 For digital signals, the signal value is rounded down to the nearest allowed level to minimize error, not up, highlighting the importance of selecting the lower value.
- 🔌 Another example is provided with voltage measurements, where increasing the number of allowed levels reduces the error in signal representation.
- 📊 Increasing the number of levels in a digital signal allows for more precise measurements and reduces the error compared to fewer levels.
- 💡 The lecture concludes with a teaser for the next session, which will discuss the necessity of digital signals despite the existence of analog and discrete time signals.
- 💬 The presenter encourages the audience to think about and share their thoughts on why digital signals are needed in the comments.
Q & A
What is the main difference between analog signals and digital signals?
-Analog signals have continuous values over time, while digital signals are discretized both in time and magnitude, meaning they can only take specific values at specific time intervals.
How is the time axis discretized in digital signals?
-In digital signals, the time axis is discretized by dividing it into equal intervals, which can be calculated using the formula delta T = (Tn - Tn-1) for any given time points Tn and Tn-1.
What is meant by discretizing the magnitude axis in digital signals?
-Discretizing the magnitude axis in digital signals involves dividing the range of possible values into a fixed number of levels, and the signal can only take values that correspond to these levels.
Can you provide an example of how temperature is measured in a digital signal?
-In the example given, the temperature at different times (T1, T2, T3, T4, T5) is measured in degrees Celsius. For a digital signal, the magnitude axis is discretized into levels such as 0, 15, 30, and 45 degrees Celsius, and the temperature at each time point is rounded down to the nearest allowed value.
Why is the lower value chosen when a measured value falls between two discrete levels?
-The lower value is chosen to minimize the error. This approach ensures that the signal value is always closer to the actual measured value than the next higher level would be.
How does the number of levels affect the error in digital signals?
-Increasing the number of levels in a digital signal reduces the error. More levels mean that the discretized values are closer to the actual continuous values, leading to a more accurate representation of the signal.
What is the significance of the statement 'the signal can take value equal to this levels only' in the context of digital signals?
-This statement emphasizes that digital signals are limited to specific, predefined values or levels. They cannot represent values that lie between these levels, which is a key characteristic of digital signals.
How is the error reduced when measuring voltage in a digital signal?
-The error is reduced by increasing the number of levels allowed for the voltage. In the example, when the voltage is discretized into more levels, a voltage of 2 volts can be accurately represented as 2 volts, reducing the error to zero.
What is the purpose of dividing the magnitude axis into fixed levels in digital signals?
-Dividing the magnitude axis into fixed levels allows for easier digital processing and storage of the signal. It also facilitates the transmission of signals with reduced error and complexity.
What is the question posed at the end of the script regarding digital signals?
-The question is: 'If we were already having analog and discrete time signals, then what is the need for digital signals?' This question prompts consideration of the advantages and applications of digital signals over analog and discrete time signals.
Outlines
📶 Understanding Digital Signals
This paragraph introduces the concept of digital signals, contrasting them with analog and discrete time signals. Digital signals discretize both time and magnitude, whereas discrete time signals only discretize time. The example of measuring temperature at different times (T1 to T5) is used to illustrate the discretization process. In the case of digital signals, the magnitude axis is also discretized into fixed levels (0, 15, 30, 45), and the signal can only take values at these levels. The importance of selecting the lower level to minimize error is emphasized, and the values of temperature at each time point are calculated accordingly.
🔌 Digital Signal Processing: Reducing Error
This paragraph further explains the difference between digital and discrete time signals using the example of voltage. It demonstrates how digital signals can only take certain values (0 and 5 volts in this case) and how errors can occur when the actual value does not match these levels. The paragraph then explores how increasing the number of levels can reduce this error. By dividing the range into more parts (0, 1.25, 2.5, 3.75, 5 volts), the error can be minimized. The example shows that a voltage of 2 volts is closer to 1.25 volts, so it is assigned that value, reducing the error. The paragraph concludes with a teaser for the next lecture, which will discuss the necessity of digital signals.
Mindmap
Keywords
💡Analog Signal
💡Discrete Time Signal
💡Digital Signal
💡Discretization
💡Magnitude Axis
💡Levels
💡Error Minimization
💡Voltage
💡Signal Processing
💡Quantization
💡Sampling
Highlights
Digital signals require discretization of both time and magnitude axes.
Discretization of time axis involves dividing it into equal intervals.
Magnitude axis discretization involves setting fixed levels for signal values.
In digital signals, the signal can only take values equal to the discretized levels.
Discrete time signals allow any magnitude value within a range.
Digital signals restrict magnitude values to specific levels, like 0, 15, 30, and 45 degrees Celsius.
When a value falls between levels, the lower level is chosen to minimize error.
Increasing the number of levels in digital signals reduces the error.
An example of discretization is given with temperature measurements.
Voltage is another example used to explain digital signal discretization.
Error in digital signals can be reduced by increasing the number of discretization levels.
The difference between discrete time signals and digital signals is highlighted.
The need for digital signals over analog and discrete time signals will be discussed in the next lecture.
The lecture invites viewers to comment their thoughts on the necessity of digital signals.
The lecture concludes with a teaser for the next session's topic.
Transcripts
in the last presentation we completed
analog and discrete time signal in this
lecture we will study digital signal in
digital signals we discretize both time
and magnitude we have to discretize both
time and magnitude axis if you remember
the discrete time signals we discretize
the time AIS but not magnitude but in
case of digital signals we have to
discretize the magnitude axis as well by
discretization I mean we have have to
divide the time XIs in equal intervals
if delta T is the interval then we can
find out this interval delta
T by T1 minus t 0 or we can have T2
minus T1 in the same way TN minus TN
minus 1 this is how we can find the
interval now the next thing that we have
to do is to discretize the magnitude
axis also this is a very simple example
in which we are trying to measure the
temperature of a city capital t is the
temperature and this is in De Cel small
T is the time in seconds and we are
measuring the temperature at T1 T2 T3 T4
and T5 if I consider the case of
discrete time signals then let's see
what we have the temperature at time T1
is equal to 9° C you can clearly see it
is equal to 9° C we have not discretized
the magnitude axis so the temperature
can take any value from 0 to 45 every
value is allowed from 0 to 45 so 9° C is
absolutely
allowed for
T2 for T2 we have
38°
C for T3 we have 24°
C for
T4 we have 15 18°
C and for T5 we have 45°
C and this is for this is for discrete
time signal right now we will consider
the case of digital signal and we have
to discretize this magnitude axis also
so let's do it I'm going to discretize
this and I will have the next
level equal to 15° C and another level
equal to 30° C so we have 0 15 30 45 as
the allowed values for the temperature
capital T this temperature can take
values equal to 0 15 3030 and 45 only we
divide the magnitude axis into fixed
number of levels and the signal can take
value equal to this level Sol this line
is very important the most important
part that you have to remember in
digital signals the signal can take
value equal to this levels only right
now we will consider the same case the
same temperatures for the same time and
we have to find out what is the value
for temperature capital T at these times
we are considering the digital signal in
this case so let's
start temperature T at time
T1 at T1 we have 9° C but 9 is not
allowed it is between 0 and 15 it is
between 0 and 15 now what we have to
take 0 or 15 the difference between 0
and 9 is 9° C and the difference between
9 and 15 is 6° C so this 9° C is near to
15° C so at first s it seems we have to
consider 15° Celsius but this is not
true to minimize the error we have to
take the lower value we have to take 0°
C this is the key point that you should
remember we don't select the higher
value we select the lower value so the
temperature T at time T1 is equal to 0°
C and the temperature T at time T2 is 38
but 38 is also not allowed it is between
3030 and 45 we again have to take 3030
because this is the lower level
so at T2 we have we have 30° C
temperature T at T3 is equal to at T3 we
have 24 24 is near to 30 but again we
have to consider the lower level so 15°
C is the answer at T4 we have 15 15 is
definitely allowed so we have 15° C at
T5 we have 45 and 45 is allowed so 45 de
C and this is the values in case of
digital signal so you can clearly see
the difference between discrete time
signals and digital signals we can have
any value of the temperature within 0 to
45 but in this case we have the value
for temperature equal to this levels
only now we will see one more example in
which we will consider the voltage
this is the time
AIS capital V is the voltage we are
considering the digital signal and uh we
have 0 volts and 5 volts as the two
values that are allowed let's say at any
time T1 the
voltage is equal
to 2 volts then voltage at T1 is equal
to 0 volts because I have already
explained you we have to consider the
lower value so I have taken 0 volts now
you can see we have error of 2 volts
because the observed voltage was 2 volts
but we are getting 0 volts so how to
overcome this error we can overcome this
error by increasing the number of levels
if we
increase the number
of
levels error will reduce this is is very
very important Point very very important
point on increasing the number of levels
arror will reduce let's see how I'm
going to divide 0 to 5 in four equal
parts so I will
have
1.25 as the next
level
2.5 and
3.75 okay these are the levels so we now
have 0 1.25 2.5 3.75 and 5 as the
allowed values for this voltage V so
voltage at time T1 is equal to is equal
to
1.25 volts because we have to consider
the lower value and 2 volt is between
1.25 and 2.5 now we can easily take 1.25
instead of zero so the error is reduced
and now we have error error of
0.75 volts only earlier the error was 2
volts but now the error is
0.75 if you increase the number of
levels more for example if I have levels
equal to 0o 1 2 3 4 and five then this 2
volt can clearly be measured as 2 volts
so voltage at T1 in this case is equal
to 2 volts and
error of zero volts is there so we have
reduced the error of 2 volts to Zer
volts by increasing the number of levels
this is all for this presentation but
there is one question if we were already
having analog and discrete time signals
then what is the need of digital
signal what
is the need of digital
signal this is the question and in the
next lecture we will discuss this need
of digital signal if you know the answer
of this question go ahead and post your
answer in the comment section this is
all for this presentation see you in the
next one
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