The signal
is bandlimited to 4 kHz. We want to sample it,
but it has been subjected to various signal processingmanipulations.
What sampling frequency (if any works) can be used
to sample the result of passing
through an RC highpass filter with
and
?
What sampling frequency (if any works) can be used to
sample the
derivative of
?
The signal
has been modulated by an 8 kHz
sinusoid having an unknown phase: the resultingsignal is
, with
and
Can the modulated signal be sampled so that the
original signal can be recovered from
the modulated signal regardless of the phase value
? If so, show how and
find the smallest sampling rate that can be used; if not,show why not.
Non-standard sampling
Using the properties of the Fourier series can ease
finding a signal's spectrum.
Suppose a signal
is periodic with period
. If
represents the signal's Fourier series
coefficients, what are the Fourier seriescoefficients of
?
Find the Fourier series of the signal
shown in
[link] .
Suppose this signal is used to sample a signal
bandlimited to
. Find an expression for and sketch the spectrum
of the sampled signal.
Does aliasing occur? If so, can a change in sampling
rate prevent aliasing;if not, show how the signal can be
recovered from these samples.
A different sampling scheme
A signal processing engineer from Texas
A&M claims to have developed an improved sampling
scheme. He multiplies the bandlimited signal by the
depicted periodic pulse signal to perform sampling (
[link] ).
Find the Fourier spectrum of this signal.
Will this scheme work? If so, how should
be related to the signal's bandwidth?
If not, why not?
Bandpass sampling
The signal
has the indicated spectrum.
What is the minimum sampling rate for this signal
suggested by the Sampling Theorem?
Because of the particular structure of this
spectrum, one wonders whether a lower sampling ratecould be used. Show that this is indeed the case, and
find the system that reconstructs
from its samples.
Sampling signals
If a signal is bandlimited to
Hz, we can sample it at
any rate
and recover the waveform exactly. This statement of the
Sampling Theorem can be taken to mean that allinformation about the original signal can be extracted
from the samples. While true in principle, you do haveto be careful how you do so. In addition to the rms
value of a signal, an important aspect of a signal isits peak value, which equals
.
Let
be a sinusoid having frequency
Hz. If we sample it
at precisely the Nyquist rate, how accurately do thesamples convey the sinusoid's amplitude? In other
words, find the worst case example.
How fast would you need to sample for the
amplitude estimate to be within 5% of the truevalue?
Another issue in sampling is the inherent amplitude
quantization produced by A/D converters. Assume themaximum voltage allowed by the converter is
volts and that it quantizes amplitudes to
bits.
We can express the quantized sample
as
, where
represents the quantization error at the
sample. Assuming the converter rounds, how large is
maximum quantization error?
We can
describe the quantization error as noise, with apower proportional to the square of the maximum
error. What is the signal-to-noise ratio of thequantization error for a full-range sinusoid?
Express your result in decibels.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product