{"id":48771,"date":"2024-04-15T22:46:05","date_gmt":"2024-04-15T22:46:05","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=48771"},"modified":"2024-04-15T22:46:05","modified_gmt":"2024-04-15T22:46:05","slug":"a-1-khz-sinusoidal-signal-is-ideally-sampled-at-1500-samples-sec-and-the-sampled-signal-is-passed-through-an-ideal-low-pass-filter-with-cutoff-frequency-800-hz-the-output-signal-has-the-frequency","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-1-khz-sinusoidal-signal-is-ideally-sampled-at-1500-samples-sec-and-the-sampled-signal-is-passed-through-an-ideal-low-pass-filter-with-cutoff-frequency-800-hz-the-output-signal-has-the-frequency\/","title":{"rendered":"A 1 kHz sinusoidal signal is ideally sampled at 1500 samples\/sec and the sampled signal is passed through an ideal low-pass filter with cutoff frequency 800 Hz. The output signal has the frequency"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a97da8612ba4\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    Zero Hz                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    0.75 kHz                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    0.5 kHz                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    0.25 kHz                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{C}}$.<\/p>\n<p>The output signal has the same frequency as the input signal, but its amplitude is attenuated by the filter. The filter attenuates frequencies above the cutoff frequency, so the output signal will have a frequency of 1 kHz, but its amplitude will be lower than the amplitude of the input signal.<\/p>\n<p>The other options are incorrect because they do not represent the frequency of the output signal. Option A is incorrect because the output signal has a frequency of 1 kHz, not 0 Hz. Option B is incorrect <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> because the output signal has a frequency of 1 kHz, not 0.75 kHz. Option D is incorrect because the output signal has a frequency of 1 kHz, not 0.25 kHz.<\/p>\n<p>Here is a more detailed explanation of the answer:<\/p>\n<p>The sampling theorem states that a continuous-time signal can be perfectly reconstructed from its samples if the sampling rate is greater than twice the highest frequency component of the signal. In this case, the input signal has <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> a frequency of 1 kHz, so the sampling rate must be greater than 2 kHz. The sampling rate in this case is 1500 samples\/sec, which is greater than twice the highest frequency component of the signal, so the input signal can be perfectly reconstructed from its samples.<\/p>\n<p>The low-pass filter attenuates frequencies above the cutoff frequency. In this case, the cutoff frequency is 800 Hz, so the filter will attenuate frequencies above 800 Hz. The output signal will therefore have a frequency of 1 kHz, but its amplitude will be lower than the amplitude of the input signal.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A 1 kHz sinusoidal signal is ideally sampled at 1500 samples\/sec and the sampled signal is passed through an ideal low-pass filter with cutoff frequency 800 Hz. 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