A 48-year-old woman from Mumbai with a history of rheumatic fever presents with palpitations and dyspnea. On examination, she has an early diastolic decrescendo murmur at the left sternal border, a wide pulse pressure (systolic 160 mmHg, diastolic 50 mmHg), and a water-hammer pulse. Chest X-ray shows cardiomegaly with a prominent ascending aorta. Which investigation is most appropriate to assess the severity of aortic regurgitation and quantify the degree of left ventricular dilatation?