## Signals and communication Homework 2(8 problems)

Given the analog signal, sampled at the rate of 8000Hz (𝑡) = 3 𝑐𝑜𝑠( 2𝜋 × 1500𝑡) + 2 𝑐𝑜𝑠( 2𝜋 × 4200𝑡) t ≥ 0 Sketch the spectrum of the sampled signal up to 20 KHz Unsampled signal spectrum is; X(jw) —————————–(3/2)————————————- ——————————1————————————— -4.2 -1.5 1.5 4.2 kHZ Sampled signal spectrum is; X(jw) ——————————————————(3/2)——————————————————— —————————————————–1————————————————————– -17.5 -16.0 -14.5 -12.4 -11.8 -9.5 -6.5 -3.8 3.8 6.5 9.5 11.8 12.4 14.5 16.0 17 khz frequency In the above spectrum, there is an overlap. (b) Sketch the recovered analog signal spectrum if an ideal low pass filter with cutoff frequency of 4KHz is used to filter the sampled signal in order to recover the original signal. X(jw) khz frequency -3.8 +3.8 2. Assuming that a 5 bit ADC channel accepts analog input ranging from 0 to 4 volts , determine the following Number of quantization levels Levels=25=32 Quantization step size Step size Quantization output level when the analog signal is 1.2 volts =20th level Binary code produced by the ADC in this case (1.2 volts input). Binary code for decimal 20 is 10100 3. MATLAB Project: Given a signal waveform (𝑡) = 3.25 𝑠𝑖𝑛( 2𝜋 × 50𝑡) + 1.25 𝑐𝑜𝑠( 2𝜋 × 100𝑡 + 𝜋/4) Sample it at 8000 samples per second and (a) Write a MATLAB program to quantize x(t) using 6 bit bipolar quantizer to obtain the Quantized signal xq, assuming the signal range is from -5 to 5. The function below performs signal quantization decoding. Here X-min will be -5 and X-max will be +5. The function is named decodingquant and is added to the path of the software. It will be called in the main program. The bits will be 6 bits since we are using a 6 bit bipolar quantizer. function deout = decodingquant(bits,Xmin,Xmax,I) le=2*bits; delta=(Xmax-Xmin)/le; deout=Xmin+I*delta; %the following function performs signal quantization decoding. This is a code for a function named quantization that performs signal quantization: function [I, out] = quantization(bits,Xmin,Xmax, value) le=2*bits; delta=(Xmax-Xmin)/le; I=round((value-Xmin)/delta); if I==le I=I-1; end if I<0 I=0; end out=Xmin+I*delta; The main program: This is where we will call our functions: quantization decodingquant We also initialize and write the code. This program quantizes the signal using 6-bits bipolar quantizer to obtain the to obtain the quantized signal x_q and plots the original and quantized signal. clc clear close all Tm=1/50; %Time period of the signal fs=8000; %This is the samplig frequency T=1/fs; %The sampling time period t=0:T:2*Tm; %This the the two period-time array. signal=3.25*sin(2*pi*50*t)+1.25*co bits=6; %6 bit quantizer as asked in the question. l=length(signal); ter initializing everything, we carry out quantization Index=zeros; quadsignal=zeros; for x=1:l [Index(x), qout]=quantization(bits,-5,5,signal(x)); end % we call the function inprder to recover signal from quantized values. % also indicate the signal range:from -5 to 5. for x=1:l quadsignal(x)=decodingquant(bits,-5,5,Index(x)); end plot(t,signal,'b') hold on stairs(t,quadsignal,'r'); ylabel('Signal') % xlabel('time (s)') legend('Original ','Quantized ') %Inorder to plot original signal and quantised signal. hold off

## Matthew Benn Eulogy

On behalf of our family, I thank everyone for being here. We truly feel supported by everyone’s kindness and prayers during this difficult time. From the day Matthew was born, he brought a joy and light to the room that nobody else could match.

## Models of Health Care Coordination

In healthcare industry today, care coordination models normally entails systematic strategies that are geared towards enhancing continuity and bridge transition gaps of care. In most cases, this employs the case of care or rather case management, whereby a responsible individual or team assist the patients in managing their medical care and navigate interactions with the health care systems (Vrijhoef, 2022). A care coordination model is operated by care coordinators who connect people to health and human service programs. Such systems play an important role in making referral, developing a personalized care plan, and in managing the exchange of information between health care providers and other human services organization. An effective and efficient care coordination model takes into account the general continuum of health care services, knowledge transmission, early child care and primary care and early intervention mechanism, food and nutrition elements and housing among other human services which are essential in improving the quality of life for the general population.

## American History

Historically, though various cultures clang with each other, some contribute to enabling a sound economy. For instance, the two documents are clear that individuals met to form European colonies in North America under various circumstances. They had different ideas, as explained in the two documents through their origin and some of the agreements which were settled together. According to the document letters from an American farmer (1782) letter 111 what is an American by J. Hector St. John de Crevecoeur, it is clear that people met to improve the economic status of the country (King 338). For instance, the documents state that the plants and hunger had taken a large portion of the area to the extent of mowing down. After some time and cooperation, plants in the country flourished, thus eradicating poverty and improvement of various industries.

## IT Management

A simple data analysis and presentation using excel functions and chart features highlight more activities on the site from people living in the U.S., mobile phones users and organic traffic. Based on this, I would advise the Chief Executive Officer in line with the following recommendations in every category of the data: Location Based on this factor, the results indicate that United States residents were the majority of visitors at 301 of the total. Japan, France and Germany followed at a distance with 64, 52 and 51 visitors, with Brazil coming last with 32. The graphical representation and summary of activities are as below:

## Child Development Theories

The Psychology of the development of children has attracted the attention of several scholars and this raises significant debates in academic discourse. The early strategies of humanity play a critical role in the formation of character and behaviors in human beings. The learning theory examines how other individuals in the formative stages of child development influence its attitudes and behavior while psychosexual development connects child development to personality development and conflict resolution among other competencies. The cognitive development theory, on the other hand, explains the knowledge acquisition process of a child from an early age. Scholars who subscribe to the socio-cultural approach examine the impact of the interaction of children with significant others as they grow up. The various theories enable the analysis of the various factors that determine the psychological and behavioral states of human development. Modern psychologists must positively critique these theories based on their observation of child development

## Therapeutic Modalities

Proper psychotherapies in the vastly evolving world come with various clinical approaches highly utilized by professional counselors to achieve their works efficiently. Based on the analysis of the SAGE encyclopedia, there are different approaches to counseling. Although they are different approaches to counseling techniques, the main role of psychotherapy includes solving the ever-increasing problems of different people in the developed world. The process of counseling and theories bases its superiority on human functionalities. There are extensive variables to consider while undertaking counseling procedures. The main problem affecting the proper execution of the counseling process in the developed world include variances in clients’ accounts and circumstances, counselor’s communications techniques, diversifications of clients, and counselor’s mood (Nusse & Clevers, 2017). Therefore, the best fit of counseling theories and approaches depends on the counselor’s ability to examine the client’s histories and situations, understand appropriate therapist’s communication techniques, invigilate their moods, and comprehend the differences between different clients. There are different theoretical approaches in conducting psychotherapy. The research centers its superiority on systemic and psychoanalytic counseling theories unveiling their importance, strengths, and their weaknesses.